Let P(x) be a statement "x+1= 3" and Q(x) be a statement "2x+1=5" Find the truth value of ∃x[P(x)^Q(x)]→[∀xp(x)∨ ∃xQ(x)]. Where domain is {1,2,3}.

• Always False
• Always True
• May be True
• Mst be False
• Always True

Let P(x) be a statement "∃x≠3(x²=9)". Find the truth value of P(x). Where domain consists of all positive number.

• Always False
• Always True
• May be True
• Mst be False
• Always False

Simplify P→Q

• P
• ¬P ∨ Q
• Q
• P ∨ ¬Q
• ¬P ∨ Q

Simplify P→¬Q

• P
• ¬P ∨ Q
• Q
• ¬P ∨ ¬Q
• ¬P ∨ ¬Q

Simplify ¬P→¬Q

• P
• ¬P ∨ Q
• Q
• P ∨ ¬Q
• P ∨ ¬Q

Simplified form of (q^r)∨(p^r)

• (q v p) ^ r
• (p ^ q) v r
• (p v q)
• ALL OF THE ABOVE
• (q v p) ^ r

Simplified form of (q→r)∨(p→r)

• (p ^ q) → r
• (q v p) → r
• (p → q)
• ALL OF THE ABOVE
• (q v p) → r

Simplest form of ¬p∧(¬r∧q)∨(q∧p)∨(q∧r)

• p
• q
• r
• None of these
• q

Simplest form of ¬p∧(¬q∧r)∨(q∧r)∨(p∧r)

• p
• q
• r
• None of these
• r

"If X then Y unless Z" is represented by which of the following formulas in prepositional logic?("¬", is negation, "∧" is conjunction, and "→" is implication)

• X∧Y)→Z
• (X∧¬Z)→Y
• X→ (Y∧Z)
• (X→Y)∧¬Z)
• (X∧¬Z)→Y