Crowdly

Which of the following statements is logically equivalent to ∀x:[(P(x)∧Q(x))→R(x)]∧∀x:[(P(x)∧R(x))→Q(x)].

∀x:[(Q(x)↔ R(x))→P(x)]

None of the option is correct.

∃x:[P(x) ∧Q(x) ∧R(x)]

∃x:[P(x)→(Q(x)↔ R(x))]

∀x:[P(x)→(Q(x)↔ R(x))]

How many free and bounded variable(s) the following expression has? (∀x:P(x)∧ Q(x))∨(∀y:[R(y)∨S(y)]∨B(w))∧A(z)

(2, 2)

None of the option is correct

(2, 3)

(3, 3)

(3, 2)

Which of the following statements is/are satisfiable?

¬[[p→(q→r)]→[(p→q)→(p→r)]]

None of the option is correct.

(p→q) ∧(p∧¬ q)

(p→q) ↔ (¬ p ∨q)

¬[[p→(q→r)]→[(p→r)→(p→q)]]

Select the correct option(s)

[p→(q→r)]→[(p→q)→(q→r)] is a tautology where p,q,r are primitive statements

[p→(q→r)]→[(p→q)→(p→r)] is a tautology where p,q,r are primitive statements

None of the option is correct

[p→(q→r)]→[(r→q)→(p→q)] is a tautology where p,q,r are primitive statements

[p→(q→r)]→[(p→q)→(r→q)] is a tautology where p,q,r are primitive statements

Choose CNF (Conjunctive Normal Formula) equivalent of the following compound statement: (¬p ∨ ¬q ) → ¬((a → ¬b) ∨ q)

(p ∨ a) ∧ (a ∨ b ) ∧ (p ∨ q) ∧∨ (a ∨ b )

(p ∨ a) ∧ (p ∨ b) ∧ (¬q ∨ p) ∧ (q ∨ a) ∧ (q ∨ b)

None of the option is correct

(p ∧ a) ∨ (a ∧ b ) v (p ∧ q) ∨ (a ∧ b )

(p ∨ a) ∧ (p ∨ b) ∧ (q ∨ p) ∧ (¬q ∨ a) ∧ (¬q ∨ b)

Choose the valid conclusions given the following premises:

∃x: [P(x)∧¬Q(x)]

∀x: [¬R(x)→¬P(x)]

∀x: [R(x)→S(x)].

∀x:Q(x)

None of the option is correct

∃x:[S(x)∧¬Q(x)]

∀x:[S(x)∧¬Q(x)]

∀x:P(x)

Which of the following represents the statement “All real numbers are complex numbers”?

∀x: [real (x)→ complex(x)]

∃x: [real (x) ∨ complex(x)]

None of the option is correct

∃x: [real (x)→ complex(x)]

∀x: [real (x) ∧ complex(x)

How many satisfiable assignments the following compound statement has? ( (p→q)∧(¬ q ∨r)∧(¬s→¬r) )→(¬p∨s)

None of the option is correct

Set A has 3 elements & set B has 4 elements . The number of injections that can be defined from A into B

144

None of the option is correct