1.) Let P Represent a True Statement, While Q and R Represent False Statements. Find The

1.) Let P represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. p ^ (qV~r).

A.) True B.) False

T ^(FV~F)= T^(FVT)=T^T=T

2.) Construct a truth table for (~q)p and submit it to the dropbox. p q ~q (~q)p T T F T T F T T F T F T F F T F

3.) Construct a truth table for (~p ^ q ) p p q ~p ~p^q (~p^q) p

T T F F F T F F F F F T T T F F F T F T 4.) Given the argument and its Euler diagram below, determine whether the syllogism is valid or invalid.

Some Tv shows are comedies. All comedies are hits. ______. Some Tv shows are hits.

The argument is valid. Here is how the Euler diagram looks like. Draw a bubble and call it Comedies.

Draw another bubble that intersects the first one and call it TV shows. Place a dot in the region where the two bubbles overlap and label it “Hit”. That’s it.

5.) Identitfy which argument is invalid. A.) Either the pando yawns or she is alert. p Vq The pando did not yawn. ~p ______Therefore, she is alert. q Valid by disjunctive syllogism

B.) If the panda yawns, then she is not alert. pq The panda is not alert. q ______Therefore, she yawned. p

Invalid by the fallacy of the converse

C.) If Tom is cooking, then I am not hungry. p q I am hungry. ~q ______Therefore, Tom is not cooking. ~p

Valid by the law of contraposition

D.) If it is hailing, then I will not go outdoors. pq If I will not go outdoors, I will not raise any money for charity. qr ______Therefore, if it is hailing, then I will not raise any money for charity. pr Valid by the law of syllogism

E.) If it is hailing, then I am not going outdoors. pq It is hailing. p ______Therefore, I am not going outdoors. q

Valid by the law of detachment.

6.) Determine if the argument is valid or invalid. Give a reason to justify your answer. If the bough breaks, then the cradle will fall. pq The bough breaks. p ______. Th cradle will fall. q .. A.) valid by the law of detachment. B.) valid by the law of contraposition. C.) Invalid by the fallacy of the converse D.) Invalid by the fallacy of the inverse E.)Valid by the law of syllogism F.) Valid by disjunctive syllogism

7.) Write the statement in symbols using the p and q given below. Then construct a truth table for the symbolic statement and select the best match. p = The mouse is in the house. q = The cat is hungry.

If the mouse is not in the house, then the cat is hungry.

A.)B.) ~(pq) It’s not the case that if the mouse is in the house then the cat is hungry.

This can be written in equivalent form as

~(pq)=~(~pVq)=p^(~q) The mouse is in the house and the cat is not hungry

Truth table p q pq ~(pq) T T T F T F F T F T T F F F T F

C.)D). ~pq If the mouse is not in the house the cat is hungry

This one can also be written in equivalent form

~pq=pVq Either the mouse is in the house or the cat is hungry

p q ~p ~pq T T F T T F F T F T T T F F T F