The statement $\style{font-family:'Times New Roman'}{\left(\neg p\right)\Rightarrow\left(\neg q\right)}$ is logically equivalent to which of the statments below?
I. $\style{font-family:'Times New Roman'}{p\Rightarrow q}$
II. $\style{font-family:'Times New Roman'}{q\Rightarrow p}$
III. $\style{font-family:'Times New Roman'}{\left(\neg q\right)\vee p}$
IV. $\style{font-family:'Times New Roman'}{\left(\neg p\right)\vee q}$
Consider the first-order logic sentence $\style{font-family:'Times New Roman'}{F:\forall x\left(\exists yR\left(x,y\right)\right)}$. Assuming non-empty logical domains, which of the sentence below are implied by F?
$\style{font-family:'Times New Roman'}{\mathrm I.\;\exists y\left(\exists xR\left(x,y\right)\right)}$
$\style{font-family:'Times New Roman'}{\mathrm{II}.\;\exists y\left(\forall xR\left(x,y\right)\right)}$
$\style{font-family:'Times New Roman'}{\mathrm{III}.\;\forall y\left(\exists xR\left(x,y\right)\right)}$
$\style{font-family:'Times New Roman'}{\mathrm{IV}.\;\neg\exists y\left(\forall y\neg R\left(x,y\right)\right)}$
Let p,q, and r be proposition and the expression $\style{font-family:'Times New Roman'}{\left(p\rightarrow q\right)\rightarrow r}$ be a contradiction. Then, the expression $\style{font-family:'Times New Roman'}{\left(r\rightarrow p\right)\rightarrow q}$ is
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 if it is raining only if it is raining and it is cold" is represented by
Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P∨Q
(v) ¬Q∨P
The number of expressions given above that are logically implied by P∧(P ⇒ Q) is__________ .
Which one of the following is NOT equivalent to $p\leftrightarrow q$?
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?
Consider the statement “Not all that glitters is gold” Predicate glitter(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?
Which one of the following propositional logic formulas is TRUE when exactly two of p, q, and r are TRUE?
Which one of the following Boolean expressions is NOT a tautology?
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?
The CORRECT formula for the sentence, “not all rainy days are cold” is
What is the logical translation of the following statement? “None of my friends are perfect.”
Which one of the following is NOT logically equivalent to $\neg \exists x(\forall y(\alpha )\wedge \forall z(\beta \left)\right)$ ?
Consider the following logical inferences.
I_{1}: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. I_{2}: 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?
What is the correct translation of the following statement into mathematical logic?
“Some real numbers are rational”
Which one of the following options is CORRECT given three positive integers x , y and z , and a predicate
$P\left(x\right)=\neg \left(x=1\right)\wedge \forall y\left(\exists z\left(x={y}_{*}z\right)\Rightarrow \left(y=x\right)\vee \left(y=1\right)\right)$
Suppose the predicate F ( x , y, t) is us ed to repr esent the statement that person x can fool person y at time t. which one of the stat ements below expresses best the meaning of the formula $\forall x\exists y\exists t\left(\neg F\left(x,y,t\right)\right)$?
Which one of the following is the most appropriate logical formula to represent the statement:
“Gold and silver ornaments are precious”
The following notations are used:
G(x): x is a gold ornament. S(x): x is a silver ornament. P(x): x is precious.
The binary operation $\tiny\Box$ is defined as follows
Which one of the following is equivalent to P $\vee $ Q?
Consider the following well-formed formulae:
I. $\neg \forall x\left(P\left(x\right)\right)$ II. $\neg \exists x\left(P\left(x\right)\right)$ III. $\neg \exists x\left(\neg P\left(x\right)\right)$ IV. $\exists x\left(\neg P\left(x\right)\right)$
Which of the above are equivalent?
Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton, and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such that equivalent (a, b) means a and b are equivalent. Which of the following first order logic statements represents the following: Each finite state automaton has an equivalent pushdown automaton.
P and Q are two propositions. Which of the following logical expressions are equivalent? I. P $\vee $ $~$ Q II.$~$ ($~$ P $\wedge $ Q) III. (P $\wedge $ Q)$\vee $ (P $\wedge $ $~$ Q) $\vee $ ($~$ P $\wedge $ $~$ Q) IV. (P $\wedge $ Q) $\vee $ (P $\wedge $ $~$ Q) $\vee $ ($~$ P $\wedge $ Q)
Let Graph(x) be a predicate which denotes that x is a graph. Let Connected(x) be a predicate which denotes that x is connected. Which of the following first order logic sentences DOES NOT represent the statement: “Not every graph is connected”?
Which of the following is TRUE about formulae in Conjunctive Normal Form?