Discrete mathematics -Determine the truth value of each of these statements if the domain consists of...

  

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Discrete mathematics -Determine the truth value of each of these statements if the domain consists of all real numbers. a) x(x3 = -1) b) 3x(x4 < x2) c) Vx((-x)2 = x2) d) Vx(2x > x) -Suppose that the domain of the propositional function P(x) consists of −5, −3,−1, 1, 3, and 5. Express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions. a) 3xP(x) b) VXP(x) c) Vx((x + 1)→ P(x)) d) 3x((x ≥ 0) A P(x)) e) 3x(P(x))X((x) → P(x)) -As mentioned in the text, the notation 3!xP(x) denotes "There exists a unique x such that P(x) is true." If the domain consists of all integers, what are the truth values of these statements? a) 3!x(x > 1) b) 3!x(x2 = 1) c) 3!x(x + 3 = 2x) d) 3!x(x = x + 1) Discrete mathematics -Determine the truth value of each of these statements if the domain consists of all real numbers. a) x(x3 = -1) b) 3x(x4 < x2) c) Vx((-x)2 = x2) d) Vx(2x > x) -Suppose that the domain of the propositional function P(x) consists of −5, −3,−1, 1, 3, and 5. Express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions. a) 3xP(x) b) VXP(x) c) Vx((x + 1)→ P(x)) d) 3x((x ≥ 0) A P(x)) e) 3x(P(x))X((x) → P(x)) -As mentioned in the text, the notation 3!xP(x) denotes "There exists a unique x such that P(x) is true." If the domain consists of all integers, what are the truth values of these statements? a) 3!x(x > 1) b) 3!x(x2 = 1) c) 3!x(x + 3 = 2x) d) 3!x(x = x + 1)

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a it is true as there is x1 in R such that x 1 1 b true as there is x 12 ... View the full answer