Mathematics · Mathematical Logic

Mathematical propositions are:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1Always true
2Either true or false✓
3Always false
4True as well as false simultaneously

Correct answer

Either true or false

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Let P and Q be two propositions. Which of the following logical expressions are equivalent? (I) P ∨ ¬Q (II) ¬(¬P ∧ Q) (III) (P ∧ Q) ∨ (P ∧ ¬Q) ∨ (¬P ∧ ¬Q) (IV) (P ∧ Q) ∨ (P ∧ ¬Q) ∨ (¬P ∧ Q)

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Let θ(x, y, z) be the statement (x + y = z), where x, y, z are real numbers. Consider two quantified statements: (i) ∀x ∀y &exists;z θ(x, y, z) (ii) &exists;z ∀x ∀y θ(x, y, z) Which of the following is correct?

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