# Math Help - I need help with these 7 discrete math proofs

1. ## I need help with these 7 discrete math proofs

2.
Let D = R. Let P(x) denote the propositional function “2x  x”. Is 8x P(x) true
D to Z+, does this change the truth
value of
8x P(x)? Why or why not?

3.
Let P(x) denote the propositional function “x2 + 1 = 0”. Can we determine whether
or not
9x P(x) is true or false without further information? Justify your answer.

4.
Let D = R, and let P(x, y) denote the propositional function “x + y = 1”.
(a) Is
(b) Is

5.
Let D denote the set of all children in the world. Let P(x, y) denote the propositional
function “
x plays with y.” Translate the following quoted statement into discrete math
notation, using quantifier symbols and
P(x, y): “Every child plays with some child.”

6.
(a) Let
D = R. Is the quantified statement 8x9y (x > y) true or false? Prove your
(b) Let
D be the set of strictly negative integers. Is the quantified statement

8
x9y (x < y)

7.
Let P(x, y, z) be a propositional function. Use the Generalized DeMorgan’s Laws for
Logic to negate the following:
(a)
8x9y8z P(x, y, z)

(b)
9x8y9z P(x, y, z)

2. Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. Start new threads as necessary for remaining questions. eg. If you have five questions, post two of them in two threads and start a new thread for the remaining one etc.