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Questions Bank (1272834 total)

Choose the main technique to prove the following statement:

3x+21=03x+21=0 has an integer solution.

T6: Constructive proof to show ∃xP(x)≡T\exists x P(x) \equiv T

T7: Two-step proof to show ∃!xP(x)≡T\exists ! x P(x) \equiv T

T1: Direct proof to show (p→q)≡T(p \to q) \equiv T

T5: Proof by cases to show ((n⋁i=1pi)→q)≡T \displaystyle \left(\left(\bigvee_{i=1}^n p_i \right) \to q \right) \equiv T

Choose the main technique to prove the following statement:

x2+2x−8=0x^2 + 2x -8=0 has integer solutions.

T6: Constructive proof to show ∃xP(x)≡T\exists x P(x) \equiv T

T7: Two-step proof to show ∃!xP(x)≡T\exists ! x P(x) \equiv T

T1: Direct proof to show (p→q)≡T(p \to q) \equiv T

T5: Proof by cases to show ((n⋁i=1pi)→q)≡T \displaystyle \left(\left(\bigvee_{i=1}^n p_i \right) \to q \right) \equiv T

Choose the main technique to prove the following statement.

√3\sqrt{3} is irrational.

T1: direct proof to show p→q≡Tp \to q \equiv T

T4: two-step proof to show p↔q≡Tp \leftrightarrow q \equiv T

T2: indirect proof by contrapostion to show p→q≡Tp \to q \equiv T

T3: indirect proof by contradiction to show p≡Tp \equiv T

Choose the main technique to prove the following statement.

If nn is even, then 5n2+6n+75n^2+6n+7 is odd.

T1: direct proof to show p→q≡Tp \to q \equiv T

T4: two-step proof to show p↔q≡Tp \leftrightarrow q \equiv T

T2: indirect proof by contraposition to show p→q≡Tp \to q \equiv T

T3: indirect proof by contradiction to show p≡Tp \equiv T

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