Quiz about Relations And Functions

Question 1

Check if the function $${f}$$ is surjective, where $$f: N 	o N$$ such that

$$f(n)=\frac{n+1}{2}, 	ext { if } n 	ext { is odd } $$

$$\quad =\frac{n}{2}, 	ext { if } n 	ext { is even }$$

Is the function injective? Justify your answer.

Accepted Answer

Covalent bond

Answer

$$No$$

Answer

$$Yes$$

Question 2

Define the relation $${R}$$ in the set $$N 	imes N$$ as follows:

For $$({a}, {b}),({c}, {d}) \in N 	imes N$$, (a, b) $${R}({c}, {d})$$ iff $${ad}={bc}$$. Prove that $${R}$$ is an equivalence relation in $$N 	imes N$$.

Accepted Answer

Covalent bond

Answer

$$Yes$$

Answer

$$No$$

Question 3

Given a non-empty set $$X$$, define the relation $${R}$$ in $${P}({X})$$ as follows:

For $${A}, {B} \in P(X),(A, B) \in R$$ iff $$A \subset B$$. Check if $${R}$$ is reflexive, transitive and not symmetric.

Accepted Answer

Covalent bond

Answer

$$Yes$$

Answer

$$No$$

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