Question

i don't have the slightest idea of what it could be

Answer 1

Let p and q be two statements as shown.

p: The carpet is rectangular.
q: The carpet is black.

Which of these correctly describes the truth value of the symbolic statement ?(p v q)^~(p^q)
It is true when p is true and q is true.
It is false when p is true and q is false.
It is true when p is false and q is true.
It is true when p is false and q is false.

Answer 2

Well, ~(p^q) becomes ~p v ~q

Answer 3

yeah i got that

Answer 4

Probably easiest to just draw up the truth table.

Answer 5

And from that point I think a really intutitive approach would be like this:
The first part says (p v q) which would mean at least one of those two true.
Then it says AND (~p v ~ q) which would mean at least one of those two false.

Answer 6

But to draw the truth table would do it also.

Answer 7

It simplifies to \(p \oplus q\)

Answer 8

^ Correct. Albeit I think that drawing the truth table may be a more intuitive approach :-)

Answer 9

hmm ok thanks :)

Answer 10

so would you say its the 3rd or 4th answer

Answer 11

I think it's best to let you figure it out.

Answer 12

i would say 3rd

Answer 13

Explain why you think that.

Answer 14

but then again it could be the 4th because my truth table i got F, T, T, T and the statement is only true if the first part is true and the second part is true or if the first part is false.

Answer 15

so it doesnt really matter what you have for the second part

Answer 16

If p is false and q is false, then (p v q) is false, which makes (p v q)^(~p v ~q) false, which makes the whole thing false.

Answer 17

You might have made a mistake on your truth table.

Answer 18

i appreciate all the help thank you ill check the truth table

Answer 19

Where E = the total statement