PLEASE SHOW WORK 1) Complete the following two truth tables. Va Ap (1) (3) (2) (

Question

PLEASE SHOW WORK

1) Complete the following two truth tables. Va Ap (1) (3) (2) (1) (3) (2) 2) Use the following p: It is raining q: l stay home today Write each of the following statement in terms of p and q using logical connectives. (Note: You may have to use negation, in some instances) a) lt is not raining implies that stay home today b) It is raining if I stay home today c) I stay home today if and only if it is raining d) It is raining only if I do not stay home today e) It is raining is a sufficient condition for me to stay home today f) It is raining is a necessary condition for me to stay home today 3) Write the contrapositive and the converse ofthe following statement If the post office is open, then it is not a national holiday a) Contrapositive: b) Converse:

Explanation / Answer

1)(pVq)^q

2a)~p->q

b)q->p

c)p <-> q

d)p->~q

e)p->q

f)q->p

3a)If it is a national holiday, then the post office is not open

b)If it is not a national holiday, then the post office is open

p q pVq ^ p T T T T T T F T T T F T T F F F F F F F (pV~q)^q p q pV~q ^ q T T T T T F T F F T T F T F F F F T F F

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