3.3 Truth tables - Conditional and Biconditional
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement. If 6^2=36, then the square root of 36 = 6
The truth value for 62=36 is true and the truth value for 36=6 is true. the compound statement is true
A compound statement that is always false is known as a _______.
self-contradiction
Is the statement (~p∧q)∧(p∨~q) a tautology, a self-contradiction, or neither?
self-contraindication
Find the truth value of each compound statement. Assume that the components r and s are false, and the component q is true. q→s
the statement is False
Find the truth value of each compound statement. Assume that the components r and s are false, and the component q is true. r→~s
the statement is True
Determine whether the statement [(p → q) ∧ (q → p)] → (p →q) is an implication.
the statement is an implication
Determine whether the statement p → p is an implication.
the statement is an implication
Determine whether the statement p → ~(~p ∧ ~q) is an implication.
the statement is an implication
Find the truth value of each compound statement. Assume that the components r and s are false, and the component q is true. (r→~s) ∧ (q→s )
the statement is false
The biconditional statement p ↔ q is _______ only when p and q have the same truth value.
true
Under what conditions is the biconditional p↔q true?
when both p and q are false and when both p and q are true
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement. Columbus Day is in March and Veterans' Day is in November, if and only if Independence Day is in April.
The compound statement is true because "Columbus Day is in March and Veterans' Day is in November" is false and "Independence Day is in April" is false.
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement. Spinach is a type of vegetable and an apple is a type of meat, if and only if bacon is a type of meat.
The compound statement is false because spinach is a type of vegetable is true an apple is a type of meat is false and bacon is a type of meat is true
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement. If a pig squeals or a bee makes honey, then a hen gobbles.
The compound statement is false because " a pig squels" is true , "a bee makes honey" is true and "a hen gobbles is false
Suppose a truth table is to be constructed for the statement ~[b→(a∧c)]. Determine the appropriate column headings and place them in a suitable order.
a b c a∧c b→(a∧c) ~[b→(a∧c)]
Suppose the truth values of the components a, b, and c are given in the compound statement ~[b→(a∧c)]. Determine an appropriate order in which to apply the truth value rules to the conjunction, negation, and conditional that appear in this statement.
conjunction, conditional, negation
The conditional statement p → q is only _______ when p is true and q is false.
false
Is the statement ~[(p∧q)↔~p] a tautology, self-contradiction, or neither?
neither
Is the statement ~[(~p∧~q)→q] a tautology, self-contradiction, or neither?
neither
You'll bake a delicious chocolate cake if and only if you follow the recipe exactly, or the surprise party will not be a success.
p <-> q ~ r (p<->q) v ~r
If today is Monday, then the aquarium is open and we can look at the turtle exhibition. p= 'today is Monday,' q= 'the aquarium is open,' r= 'we can look at the turtle exhibit. Write the statement in symbolic form.
p → (q ^ r)
