Propositional Logic
Q21.
Which one of the following propositional logic formulas is TRUE when exactly two of p, q, and r are TRUE?Q22.
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 qQ23.
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?Q24.
What is the correct translation of the following statement into mathematical logic? "Some real numbers are rational"Q25.
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?Q27.
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?Q28.
Consider the following two statements. S1: If a candidate is known to be corrupt, then he will not be elected S2: If a candidate is kind, he will be elected Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?Q29.
Let p, q, r denote the statements "It is raining ," It is cold", and " It is pleasant," respectively. Then the statement "It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold" is represented byQ30.
In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking, the person replies the following "The result of the toss is head if and only if I am telling the truth." Which of the following options is correct?