Another example from my textbook that I can't quite figure out. Let p(x), q(x) denote the following open statements.
p(x): x ≤ 3
q(x): x + 1 is odd
If the universe consists of all integers, what are the truth values of the following statements?
a) q(1)
b) ¬p(3)
c) p(7) v q(7)
d) p(3) ^ q(4)
e) ¬(p(-4) v q(-3))
f) ¬p(-4) ^ ¬q(-3)
This isn't homework. I am taking a math class in about a month and am studying a textbook that I believe will help. Am I posting in the right forum? The questions I am posting are ones that didn't have great examples and are confusing to me.
Okay I learned a bit more about these symbols.
Are these right?
b) ¬p(3): not 3 ≤ 3 = False
c) p(7) v q(7): 7 ≤ 3 or 7 + 1 is odd...both are false, so it is False
d) p(3) ^ q(4): 3 ≤ 3 and 4 + 1 is odd...one is true, one is false, so it is False (since both must be true)
e) ¬(p(-4) v q(-3)): ¬(-4 ≤ 3 or -3 + 1 is odd)...one is false, one is true, so it is True
f) ¬p(-4) ^ ¬q(-3): ¬ -4 ≤ 3 and ¬ -3 + 1 is odd...one is false, one is true, so it is False
You are missing the "not" at the start aren't you?e) ¬(p(-4) v q(-3)): ¬(-4 ≤ 3 or -3 + 1 is odd)...one is false, one is true, so it is True
" " is true, "-3+ 1 is odd" is false so the statement "one of p(-4) OR q(3) is true" is true which means that "NOT....." is false.
Ohhh i see now. Thank you so much for that. What I was doing was saying the first is true and second is false, and then just switching them. But I see that you are supposed to conclude that the entire statement is either true or false, and then use the negation symbol.