Propositional Logic


Q21.

The statement (\neg p)\Rightarrow (\neg q) is logically equivalent to which of the statements below? I. p\Rightarrow q II. q \Rightarrow p III. (\neg q)\vee p IV. (\neg p)\vee q
GateOverflow

Q22.

Which one of the following Boolean expressions is NOT a tautology?
GateOverflow

Q23.

Which one of the following is NOT equivalent to p\leftrightarrow q?
GateOverflow

Q24.

Let p,q, r, s represent the following propositions. p: x\in{8,9,10,11,12} q: x is a composite number r: x is a perfect square s: x is a prime number The integer x\geq2 which satisfies \neg((p\Rightarrow q)\wedge (\neg r \vee \neg s)) is ________.
GateOverflow

Q25.

Which one of the following is NOT logically equivalent to \neg \exists x(\forall y(\alpha )\wedge \forall z(\beta ))?
GateOverflow

Q26.

Given thatB(a) means "a is a bear"F(a) means "a is a fish" andE(a,b) means "a eats b"Then what is the best meaning of\forall x[F(x) \rightarrow \forall y(E(y, x) \rightarrow b(y))]
GateOverflow

Q27.

Let p, q, and r be propositions and the expression (p\rightarrowq)\rightarrowr be a contradiction. Then, the expression (r\rightarrowp)\rightarrowq is
GateOverflow

Q28.

The CORECT formula for the sentence, "not all rainy days are cold" is
GateOverflow

Q29.

Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate P(x)=\neg (x=1)\wedge \forall y(\exists z(x=y*z))\Rightarrow (y=x)\vee (y=1)
GateOverflow

Q30.

Consider the following logical inferences. I1: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. I2: If it rains then the cricket match will not be played. It did not rain. Inference: The cricket match was played. Which of the following is TRUE?
GateOverflow