Test: Predicates and Quantification - Engineering Mathematics MCQ

Clarification: For n = 0, 4n = 3n hence, it is true.

Clarification: Domain may be limited to your class or may be whole world both are good as it satisfies universal quantifier.

Clarification: For every person x, if comedian then x is funny.

Clarification: Because P(x) is false for every real number x, the existential quantification of Q(x), which is ∃xP(x), is false.

Clarification: Q(x) is not true for every real number x, because, for instance, Q(6) is false. That is, x = 6 is a counterexample for the statement ∀xQ(x). This is false.

Clarification: There is no student who spends more than 2 hours in playing polo.

Clarification: For some x, x is friend and funny.

Clarification: Because “x > 2” is sometimes true—for instance, when x = 3–the existential quantification of R(x), which is ∃xR(x), is true.

Clarification: There are no elements in the domain for which the statement is false.

Clarification: Put x = 9, 9 > 7 which is true.