Propositional Logic


Q21.

What is the logical translation of the following statement? "None of my friends are perfect."
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Q22.

Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT?
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Q23.

Which one of the following is NOT equivalent to p\leftrightarrow q?
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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 ________.
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Q25.

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))]
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Q26.

Which one of the following is NOT logically equivalent to \neg \exists x(\forall y(\alpha )\wedge \forall z(\beta ))?
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Q27.

Let p, q, and r be propositions and the expression (p\rightarrowq)\rightarrowr be a contradiction. Then, the expression (r\rightarrowp)\rightarrowq is
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Q28.

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