Discrete Math: Long Examination 1 - Modified True or False

Using the domination law, it is proven that p ∧ p is logically equivalent to p

[(p∨q)∧(p→r)∧(q→r)]→r is not a tautology

[(p→q)∧(q→r)]→(p→r)  is not a tautology

¬p ↔ q and p ↔ ¬q are logically equivalent

Given 6 propositional variables, the number of rows in a truth table is 32

In P(x) equation 4x⁴ + 3x³ + 5x² + 2 > 110, the truth value of P(2) is false

For every real number x there exists a real number z such that x is less than y is translated as ‚∀x∃y(x < y)

The truth value of ∀x(x != 0→ ∃y(xy=1)) is false if the domain of each variable consists of all real numbers

The truth value of ∃x∃y(x+2y=2 ∧ 2x+4y=5) is true if the domain of each variable consists of all real numbers

The truth value of the statement ∃x ∀y (x ≤ y 2 ) is false if the domain is positive real numbers