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 qQ24.
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 ________.Q25.
Which one of the following is NOT logically equivalent to \neg \exists x(\forall y(\alpha )\wedge \forall z(\beta ))?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))]Q27.
Let p, q, and r be propositions and the expression (p\rightarrowq)\rightarrowr be a contradiction. Then, the expression (r\rightarrowp)\rightarrowq isQ29.
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)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?