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Questions Bank (1395552 total)

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

Consider a function f:R→Rf:R→Rf: R \to R, f(x)=2x+8f(x)=2x+8f(x) = 2x+8.

Determine the correct sequence to prove the following statement.

ff is surjective.

If a statement is not used in the proof, you have to choose "Not used".

Consider an arbitrary real number yy.

Assume f(x)=yf(x)=y.

2x+8=y2x+8=y

Consider two arbitrary real numbers aa and bb.

ff is injective

a=ba = b

2a+8=2b+82a+8=2b+8

Assume that f(a)=f(b)f(a)=f(b).

ff is surjective

x=y−82x = \frac{y-8}{2} exists