Homework 3.1

Let​ p, q, and r represent the following statements. ​p:It is time to sleep. ​q:It is late. ​r:I am tired. Write the following compound statement in its symbolic form. If I am tired and it is late​, then it is time to sleep.

( r ^ q) p

Write the negation of the statement. Some cats do not have claws.

All cats have claws.

Let​ p, q, and r represent the following simple statements. ​p: It is Tuesday. ​q: I study. ​r: The taxes are high. Write the symbolic statement in words. (q r) ^ p

If I study then the taxes are high, and it is Tuesday

Let p and q represent the following simple statements. ​p: It is Tuesday. ​q: It is time to sleep. Write the symbolic statement ~(p∧q) in words.

It is not true that it is Tuesday and it is time to sleep

Let p represent the following statement. ​p: Vesuvius is a volcano in Italy. Express the symbolic statement​ ~p in words.

Vesuvius is not a volcano in Italy

Let p and q represent the following simple statements. ​p: I get an A. ​q: This is an octopus. Write the following compound statement in its symbolic form. I get an A and this is an octopus

p^q

Let p and q represent the following simple statements. ​p: I work hard. ​q: I get an A. Write the following compound statement in its symbolic form. I work hard and I get an A.

p^q

Let p and q represent the following statements. ​p: The test is today. ​q: Salvadore Dali painted the Sistine Chapel. Express the following statement symbolically. The test is not today

~p

Let p and q represent the following simple statements. ​p: The stove is hot. ​q: It is snowing outside. Write the following compound statement in its symbolic form. If the stove is not hot​, then it is not snowing outside.

~p →~q

Let​ p, q, and r represent the following simple statements. ​p: It is time to sleep. ​q: The stove is hot. ​r: The job pays well. Write the following compound statement in its symbolic form. It is time to sleep and the stove is hot​, or the job pays well.

(p^q) Vr

Let​ p, q, and r represent the following simple statements. ​p: This is an octopus. ​q: I study. ​r: The chair is broken. Write the following compound statement in its symbolic form. This is an octopus and I study​, or the chair is broken.

(p^q) Vr

Let​ p, q, and r represent the following simple statements. ​p: I get an A. ​q: The job pays well. ​r: This is an octopus. Write the symbolic statement in words. ~r (q ^ p)

If this is not an octopus, then the job pays well and I get an A

Let p and q represent the following simple statements. ​p: It is time to sleep. ​q: The play is boring. Write the symbolic statement ~(q∨p) in words.

It is not true that the play is boring or it is time to sleep

Let p and q represent the following simple statements. ​p: The taxes are high. ​q: It is time to sleep. Write the symbolic statement ~(p∧q) in words.

It is not true that the taxes are high and it is time to sleep

Let​ p, q, and r represent the following simple statements. ​p: It is Tuesday. ​q: It is snowing outside. ​r: I work hard. Write the symbolic statement in words. (p V q) ^ ~r

It is tuesday or it is snowing outside, and I do not work hard

Write the negation of the statement. No dogs have hair.

Some dogs have hair.

Write the negation of the statement. No motorcycles have three wheels.

Some motorcycles have three wheels.

Write the negation of the statement. All pigs fly.

Some pigs do not fly.

Let​ p, q, and r represent the following simple statements. ​p: This is an octopus. ​q: The play is boring. ​r: I study. Write the symbolic statement in words. ~p ^ (q V r)

This is not an octopus, and the play is boring or I study

Let p and q represent the following simple statements. ​p: I complete my homework. ​q: I get a raise Write the following compound statement in symbolic form. I do not complete my homework or I get a raise

~pVq

Let p and q represent the following statements. ​p: One does one's best. ​q: Paris is the capital of Arkansas. Express the following statement symbolically. Paris is not the capital of Arkansas.

~q

Let p and q represent the following statements. ​p: It is Tuesday. ​q: I am working. Write the following compound statement in its symbolic form. I am not working if and only if it is Tuesday.

~q ⇔ p

Let p and q represent the following statements. ​p: The taxes are high. ​q: The job pays well. Write the following compound statement in its symbolic form. The job does not pay well if and only if the taxes are high.

~q ⇔ p

Write the statement in symbolic form. Let p and q represent the following statements. ​p: The canoes are in the river. ​q: The hotdogs are cooked. The hotdogs are not cooked or the canoes are not in the river.

~qv~p

Write the statement in symbolic form. Let p and q represent the following statements. ​p: The sleeping bags are unpacked. ​q: The firewood is gathered. The firewood is not gathered or the sleeping bags are not unpacked

~qv~p

Write the statement in symbolic form. Let p and q represent the following statements. ​p: The ocean is salty. ​q: The waves are big. It is false that the ocean is salty or the waves are big.

~​(p ∨ q)

Write the statement in symbolic form. Let p and q represent the following statements. ​p: The pizza is delicious. ​q: The cheese is cold. It is false that the pizza is delicious or the cheese is cold.

~​(p ∨ q)