1. (p v q) → (q → q) = r 2. (p A ¬q) v q = p V q 3. -(p A q) A q = ¬p A q

Create a universal conditional statement in the domain of square roots of positive integers that is vacuously true. [A conditional is vacuously true if, and only if, the truth set of the hypothesis is empty.]

Suppose A is open. Consider the following statements: (i) If finitely many points are removed from A, then A is still open. (ii) If infinitely many points are removed from A, then A is still open. Which one is correct.

(a) Prove by using logical arguments (not by sketching Venn diagrams) that (AUB) = Aªn Bª.

Use truth sets to prove or disprove the following quantified statements. a) Let D = {1, 3, 4} Let P(x) be the predicate "x2 + 2x > 0". Show that Va E D, x? + 2x > 0 b) Let D = {- 1, 0, 1, 3, 4} Let P(x) be the predicate "x + 2x > 0". Show that Vx E D, x? + 2x > 0 is false.

Determine if the conclusion follows logically from the premises.  You must submit proof either with an Euler diagram, a TT, or state a standard form of argument as it applies to the premises. Premise: No passive individuals are folks who live well.Premise: All self-actualized persons are folks who live well.Conclusion: No self-actualized persons are passive individuals. Valid argument Invalid argument

(b) Consider the following statement: For all a € R, {x ≤ Q : x² = a} = 0 i. Which of "if", "only if", "iff" in your claim. ii. Which of "if", "only if", "iff" in your claim. a & Q. make this a true statement? Prove make this a false statement? Prove

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