Discrete Mathematics
Q221.
Which of the following first order formulae is logically valid? Here \alpha(x) is a first order formula with x as a free variable, and \beta is a first order formula with no free variable.Q222.
P and Q are two propositions. Which of the following logical expressions are equivalent? I. P\vee \sim Q II.\sim (\sim P \wedge Q) III.(P \wedge Q)\vee (P\wedge \sim Q)\vee (\sim P\wedge \sim Q) IV. (P\wedge Q)\vee \vee (P\wedge \sim Q)\vee (\sim P\wedge Q)Q223.
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: taller (x, y) is true if x is taller than y.Q224.
Consider the following first order logic formula in which R is a binary relation symbol. \forall x \forall y(R(x, y) \Longrightarrow R(y, x)),The formula isQ225.
Let P(x) and Q(x) be arbitrary predicates. Which of the following statements is always TRUE?Q226.
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened.Q228.
Consider the following propositional statements: P1:((A\wedge B)\rightarrow C)\equiv (A\rightarrow C)\wedge (B\rightarrow C) P2:((A\vee B)\rightarrow C)\equiv (A\rightarrow C)\vee (B\rightarrow C) Which one of the following is true?Q229.
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"?Q230.
What is the first order predicate calculus statement equivalent to the following? Every teacher is liked by some student