Answer to Question #247471 in Discrete Mathematics for Mathica

Question

(3). If p, q, and r denote the following propositions:

p : 2 < 3.

q : The cube of -1 is -1.

r : The empty set contains one element.

express the following propositions symbolically.

(a) If 2 ≥ 3, then the cube of -1 is -1.

(b) If and only if 2 < 3 or the cube of -1 is not -1 then the empty

set does not contain one element.

(c) The empty set contains one element and, if 2 ≥ 3, then the

cube of -1 is -1.

Answer 1

Solution:

p : 2 < 3.

q : The cube of -1 is -1.

r : The empty set contains one element.

(a) If 2 ≥ 3, then the cube of -1 is -1.

$\sim p\rightarrow q$

(b) If and only if 2 < 3 or the cube of -1 is not -1 then the empty set does not contain one element.

$(p \vee \sim q) \leftrightarrow \sim r$

(c) The empty set contains one element and, if 2 ≥ 3, then the

cube of -1 is -1.

$(r \wedge\sim p) \rightarrow q$