Question

The truth-value of p is False, the truth-value of q is True, and the truth-value of r is True.
Determine the truth-value of the following compound statement: ~ (p∨r)∧~q?

Answer 1

it should read ~(p V r) ^ ~q

Answer 2

it just wants to know if the statement is true or false

Answer 3

work out one operation at a time

Answer 4

parenthesis first right?

Answer 5

yes

Answer 6

I'm getting false

Answer 7

p, q, r, (p∨r), ~(p∨r), ~q, ~ (p∨r)∧~q
F T T

Answer 8

what do you get for the first bit ;
(p∨r)

Answer 9

P or q is true

Answer 10

it is p or r

Answer 11

So don't count the ~ before the parenthesis ~(p V r)?

Answer 12

always do the inside of the parenthesises first

Answer 13

(p∨r)

(F∨T)

Answer 14

ok so if one of these is false the statement can't be true unless it in ~ which it has so now the statement is true? looking at my note too haha

Answer 15

am I right?

Answer 16

we have:
\[P \vee Q = true\]

Answer 17

so:
\[\neg \left( {P \vee Q} \right) = false\]

Answer 18

furthermore:
\[\neg Q = false\]

Answer 19

then:
\[\neg \left( {P \vee Q} \right) \wedge \neg Q = false \wedge false = ...?\]

Answer 20

Are you asking me or telling me thats the answer?

Answer 21

?