Propositional Logic
Q11.
The binary operator \neq is defined by the following truth table. Which one of the following is true about the binary operator \neq?Q12.
Choose the correct choice(s) regarding the following proportional logic assertion S:S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))[MSQ]Q13.
Consider the statement "Not all that glitters is gold" Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?Q14.
Consider the first-order logic sentence F:\forall x(\exists yR(x,y)). Assuming non-empty logical domains, which of the sentences below are implied by F? I. \exists y(\exists xR(x,y)) II. \exists y(\forall xR(x,y)) III. \forall y(\exists xR(x,y)) IV. \neg \exists x(\forall y\neg R(x,y))Q16.
What is the logical translation of the following statement? "None of my friends are perfect."Q17.
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?Q19.
Geetha has a conjecture about integers, which is of the form\forall x\left [P(x)\Rightarrow \exists yQ(x,y) \right ] where P is a statement about integers, and Q is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha's conjecture?Q20.
Consider the first-order logic sentence \varphi \equiv \exists s\exists t\exists u\forall v\forall w\forall x\forall y\varphi (s,t,u,v,w,x,y) where \varphi (s,t,u,v,w,x,y) is a quantifier-free first-order logic formula using only predicate symbols, and possibly equality, but no function symbols. Suppose \varphi has a model with a universe containing 7 elements. Which one of the following statements is necessarily true?