Are these statements true or false The universe of discourse

Are these statements true or false? The universe of discourse is . Explain how you determined your solution.

x(5 < x < 10 abc(a² + b² + c² = x)).

!x((x – 4)² = 36).

!x((x – 11)² = 49).

xy((x y) (x – 4)² = 36) (y – 4)² = 36).

Solution

Build one truth table for f ! (r ^ h) and (f ! r) ^ h. 4 f r h r ^ h f ! r f ! (r ^ h) (f ! r) ^ h T T T T T T T T T F F T F F T F T F F F F T F F F F F F F T T T T T T F T F F T T F F F T F T T T F F F F T T F 2.1.1: Build a truth table to verify that the proposition (p $ q)^(¬p^q) is a contradiction. p q p $ q ¬p ¬p ^ q (p $ q) ^ (¬p ^ q) T T T F F F T F F F F F F T F T T F F F T T F F 2.3.1: Use a truth table to show that the propositions p $ q and ¬(p2q)