Following compound Proposition"(P^(P⇒Q)^(¬P∨R)^(R⇒X))⇒X" iS

• Tautology
• Satisfiable
• Both Tautology & Satisfiable
• Contradiction
• Both Tautology & Satisfiable

Following compound Proposition"(P^(P⇒Q)^(¬P⇒R)^(R⇒X))⇒X" iS

• Tautology
• Satisfiable
• Both Tautology & Satisfiable
• Contradiction
• Satisfiable

Express the statement "There is a person in this world who has played every video game of this year" using Quantifiers.Let P(x,y) denotes x has played video game y in this year.

• ∀x∀yP(x,y)
• ∀x∃yP(x,y)
• Both
• ∃x∀yP(x,y)
• ∃x∀yP(x,y)

Check which of the following is valid. 1. (¬p∧q)∧(¬p∨q)→q 2. (p∧q)∧(p∨q)→¬p

• 1
• 2
• Both 1 and 2
• None of these.
• 1

Conclusion of premises P ∧(¬P→Q) is

• P
• Q
• P ∧ Q
• P∨Q
• P∨Q

Conclusion of premises P ∧(¬P∨Q) is

• P
• Q
• P ∧ Q
• P∨Q
• Q

The statement ¬P→¬Q is logically equivalent to

• P→Q
• P→¬Q
• P ∨ ¬Q
• ¬P ∨ Q
• P ∨ ¬Q

The statement ¬P→Q is logically equivalent to

• P→Q
• P→¬Q
• ¬P ∨ Q
• ¬P ∧ ¬Q
• ¬P ∧ ¬Q

If sinθ=12/15 then value of cosθ will be

• 12/15
• 15/12
• 9
• 5
• 9

If sinθ=12/13 then value of cosθ will be

• 12/15
• 15/12
• 9
• 5
• 5