Question

Express the following relations in set builder notation:

Answer 1

Answer:

$S=\{x,y\in R, x\leq y\}$

$S=\{x,y\in Z, gcd(x,y)=x\ when\ x$

$S=\{x,y\in Z, x\neq y \}$

$S=\{P,Q\ \text{are sets such that}P\subseteq Q \}$

Step-by-step explanation:

Consider the provided information.

We need to Express the following relations in set builder notation.

Part (A)

One number is less than or equal to another.

Let say One number is x and another number is y.

The statement can be written as: x≤y

Let S be required set. Now, express the above statement in set builder notation,

$S=\{x,y\in R, x\leq y\}$

Part (B)

One integer is a factor of another.

Let say One number is x and another number is y.

If one integer is factor of other then the greatest common factor of x and y should be x.

Let S be required set. Now, express the above statement in set builder notation,

$S=\{x,y\in Z, gcd(x,y)=x\ when\ x$

Part (C)

Two integers are unequal

Let say One number is x and another number is y.

Let S be required set. Now, express the above statement in set builder notation,

$S=\{x,y\in Z, x\neq y \}$

Part (D)

One set is a subset of another.

Let say One set is P and another set is Q.

Let S be required set. Now, express the above statement in set builder notation,

$S=\{P,Q\ \text{are sets such that}P\subseteq Q \}$