Statement A: Let Q(x) be a predicate and D the domain of x. An existential statement is a statement of the form “∃!x ∈ D such that Q(x).”

Statement B: It is defined to be true if, and only if Q(x) is true for at least one x in D.

Statement A: The notation P(x) ⇒ Q (x) means that that P(x) and Q(x) have identical truth sets

Statement B: The notation P(x) ⇔ Q (x) means that every element in the truth set of P(x) is in the truth set of Q(x)

Statement A: The negation of a statement of the form ∀x in D, Q (x) is logically equivalent to statement of the form ∀x in D such that ∼Q(x).

Statement B: ∼(∀x ∈ D, Q(x)) ≡ ∃x ∈ D such that ∼Q(x).

Statement A: ∀ nonzero real numbers u, ∃ a real number v such that uv = 1.

Statement B: ∃ a real number c such that ∀ real numbers d, cd  != 1.

Statement A: In bit operators’ truth value, 0 signifies True and 1 signifies false

Statement B: In getting the number of rows for the truth table, the formula is 2^n where n is the number of proposition variables

Statement A: using the truth table, the propositions (p ∨ q ∨ r) ∧ (¬p ∨ ¬q ∨ ¬r) is true when at least one of the p, q, and r is true and at least one is false

Statement B: On the same proposition as Statement A, the value is true when all three variables have the same truth value

Statement A: for the bit strings 1011110 and 010001, it is possible to get the bitwise XOR

Statement B: Using the same bit strings as Statement A, it is also possible to get its bitwise AND

Statement A: A compound proposition that is always true is called Contradiction

Statement B: A compound proposition that is always false is called Contingent

Statement A: Let Q(x) be a predicate and D the domain of x. A universal statement is a statement “∀x ∈ D, Q(x).”

Statement B: It is defined to be true if sometimes Q(x) is true in D.