Question

p: It snows tonight.
q: I will stay home.

Use negation (~), conjunction (˄), disjunction (˅), and/or implication (→) to construct a logical equivalence of p→q.

Answer 1

This is converse, contrapositive and inverse, right?

Answer 2

I'm not sure, to be honest.

Answer 3

It's discrete math, if that helps at all.

Answer 4

So... The converse is "If it snows tonight, I will stay home." The contrapositive is "If it doesn't snow tonight, then I won't stay home." The inverse is: "If I won't stay home tonight, then it won't snow."

Answer 5

I think I have to make an equation that looks sort of like this: p v q or ~p v q. I'm not really clear on what is wanted in this problem and my book isn't much help.

Answer 6

Original Statement
If P then Q
Negation Statement
If NOT P then NOT Q
Converse Statement
if Q then P
Contrapositive Statement
if NOT Q then NOT P

Answer 7

Conditional: ~a -> ~b
Converse: ~b -> ~a

Answer 8

P ^ Q is P AND Q (both)
P V Q is P OR Q (one or the other)

Answer 9

I think my book uses different terms. I remember
original statement
negation is the negative version of the original statement
converse is the reversed version of the original statement
and contrapositive is the negative reversed version of the original statement.

Answer 10

so we have to go to P -> Q
P implies Q using some techniques from or and and statements... like a truth table.

Answer 11

Yes like truth tables. I guess my question is not so much how to do this, but more of what the question is asking me to do. The terminology seems to be different in other places I look, so I guess that is why I was confused.

Answer 12

P Q P - > Q
T T T
T F F
F T T
F F T

that's the implies table

Answer 13

Thank you! That actually helped.

Answer 14

so if P is true Q is true... implies will give a True
if P is true, Q is false implies will give a False
if P is false Q is true implies will give a true
if P is false Q is false implies give a true.

Answer 15

Thank you!

Answer 16

you're welcome :)