Practicing with the Square of Opposition (Modern and Traditional)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the O-proposition is true, the A-proposition is_______.
False. This inference is valid on both interpretations. A- and O-propositions are contradictories. They cannot be simultaneously true or simultaneously false. Hence, if one is true, the other must be false, and vice-versa. Here are some examples: Some stringed instruments are not guitars. (True) All stringed instruments are guitars. (False) Some carnivores are not vegan. (True) All carnivores are vegan. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the I-proposition is true, the E-proposition is_______.
False. This inference is valid on both interpretations. E- and I-propositions are contradictories. They cannot be simultaneously true or simultaneously false. Hence, if one is true, the other must be false, and vice-versa. Here are some examples: Some pit bulls are dogs. (True) No pit bulls are dogs. (False) Some Blue Jays are birds. (True) No Blue Jays are birds. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the I-proposition is false, the A-proposition is_______.
False. This inference is valid only on the traditional interpretation. Both sub- and superalternation are not allowed on the modern interpretation. Here is an example: Some cats are dogs. (False) All cats are dogs. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the O-proposition is false, the E-proposition is_______.
False. This inference is valid only on the traditional interpretation. Both sub- and superalternation are not allowed on the modern interpretation. Here is an example: Some pit bulls are not dogs. (False) No pit bulls are dogs. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the A-proposition is true, the E-proposition is_______.
False. This inference is valid only on the traditional interpretation. If a universal proposition is true, its contrary must be false. Here are some examples: All beagles are dogs. (True) No beagles are dogs. (False) All guitars are stringed instruments. (True) No guitars are stringed instruments. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the E-proposition is true, the A-proposition is_______.
False. This inference is valid only on the traditional interpretation. If a universal proposition is true, its contrary must be false. Here are some examples: No cats are dogs. (True) All cats are dogs. (False) No Toyotas are Hondas. (True) All Toyotas are Hondas. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the O-proposition is false, the A-proposition is_______.
True. This inference is valid on both interpretations. A- and O-propositions are contradictories. They cannot be simultaneously true or simultaneously false. Hence, if one is true, the other must be false, and vice-versa. Here are some examples: All stringed instruments are guitars. (False) Some stringed instruments are not guitars. (True) Some Blue Jays are not birds. (False) All Blue Jays are birds. (True)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the I-proposition is false, the E-proposition is_______.
True. This inference is valid on both interpretations. I- and E-propositions are contradictories. They cannot be simultaneously true or simultaneously false. Hence, if one is true, the other must be false, and vice-versa. Here are some examples: Some wind instruments are guitars. (False) No wind instruments are guitars. (True) Some carnivores are vegan. (False) No carnivores are vegan. (True)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the I-proposition is false, the O-proposition is_______.
True. This inference is valid on the traditional interpretation of the Square of Opposition only. (The modern interpretation does not allow inferences from a particular proposition to its subcontrary.) Here are some examples: Some birds are cats. (False) Some birds are not cats. (True) Some ducks are not feathered creatures. (False) Some ducks are feathered creatures. (True)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the O-proposition is false, the I-proposition is_______.
True. This inference is valid on the traditional interpretation of the Square of Opposition only. (The modern interpretation does not allow inferences from a particular proposition to its subcontrary.) Here are some examples: Some birds are cats. (False) Some birds are not cats. (True) Some ducks are not feathered creatures. (False) Some ducks are feathered creatures. (True)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the I-proposition is true, the O-proposition is_______.
Undetermined on both interpretations. When a particular claim is true, the structure reflected in that value does not force its subcontrary to be true or false. Here are some examples: Some dogs are pit bulls. (True) Some dogs are not pit bulls. (True) Some trucks are vehicles. (True) Some trucks are not vehicles. (False) Some medical doctors are not surgeons. (True) Some medical doctors are surgeons. (True) Some apples are not oranges. (True) Some apples are oranges. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the O-proposition is true, the I-proposition is_______.
Undetermined on both interpretations. When a particular claim is true, the structure reflected in that value does not force its subcontrary to be true or false. Here are some examples: Some dogs are pit bulls. (True) Some dogs are not pit bulls. (True) Some trucks are vehicles. (True) Some trucks are not vehicles. (False) Some medical doctors are not surgeons. (True) Some medical doctors are surgeons. (True) Some apples are not oranges. (True) Some apples are oranges. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the O-proposition is true, the E-proposition is_______.
Undetermined on both interpretations. When a particular proposition is true, its corresponding superaltern may be true or it may be false. Here are some examples: Some cellos are not wind instruments. (True) No cellos are wind instruments. (True) Some reptiles are not frogs. (True) No reptiles are frogs. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the I-proposition is true, the A-proposition is_______.
Undetermined on both interpretations. When a particular proposition is true, its corresponding superaltern may be true or it may be false. Here are some examples: Some pit bulls are dogs. (True) All pit bulls are dogs. (True) Some stringed instruments are cellos. (True) All stringed instruments are cellos. (False)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the A-proposition is false, the I-proposition is_______.
Undetermined on both interpretations. When a universal proposition is false, its corresponding subaltern may be true or it may be false. Here are some examples: All cats are rabbits. (False) Some cats are rabbits. (False) All stringed instruments are violins. (False) Some stringed instruments are violins. (True)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the E-proposition is false, the O-proposition is_______.
Undetermined on both interpretations. When a universal proposition is false, its corresponding subaltern may be true or it may be false. Here are some examples: No violins are stringed instruments. (False) Some violins are not stringed instruments. (False) No dogs are beagles. (False) Some dogs are not beagles. (True)
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the A-proposition is false, the E-proposition is_______.
Undetermined on both interpretations. When a universal proposition is false, the logical structure reflect by that value does not force its contrary to be true or false: All dogs are beagles. (False) No dogs are beagles. (False) OR No birds are Cardinals. (False) All birds are Cardinals. (False) Contraries can have opposite truth values, when the premise is false: All flutes are stringed instruments. (False) No flutes are stringed instruments. (True) OR No Coca-Colas are sodas. (False) All Coca-Colas are sodas. (True) Since the contrary can be true or false, when the premise is false, we cannot draw a necessary inference.
Instructions: 1) Determine whether or not the following inference is valid on BOTH interpretations of the square of opposition (modern and traditional); if the inference is valid, explain why; and 3) if the inference is undetermined, explain why. If the E-proposition is false, the A-proposition is_______.
Undetermined on both interpretations. the logical structure reflect by that value does not force its contrary to be true or false: All dogs are beagles. (False) No dogs are beagles. (False) OR No birds are Cardinals. (False) All birds are Cardinals. (False) Contraries can have opposite truth values, when the premise is false: All flutes are stringed instruments. (False) No flutes are stringed instruments. (True) OR No Coca-Colas are sodas. (False) All Coca-Colas are sodas. (True) Since the contrary can be true or false, when the premise is false, we cannot draw a necessary inference.
