Given sets A,B,C be defined as follows

A={\(ninZ|n=2p\), for some integers p}

B={\(m inZ|m=2q-1\),for some integers q}

C={\(kinZ|k=4r\),for some integers r}

Given sets A,B,C be defined as follows

A={\(ninZ|n=2p\), for some integers p}

B={\(m inZ|m=2q-1\),for some integers q}

c={\(kinZ|k=4r\),for some integers r}

Steps:

Prove A=B

2p=2q-2

p=q-1

Given p and q are the integers.

If q is an integer, then (q-1) is also an integer.

Since, if take q = p-1 then A and B are equal.

Hence, A = B if q = p-1

Prove in the following that A = C.

n = 2p

and

k = 4r

Given, p and r are the integers.

Take p = 1 and r = 1, then

n = 2

and

k = 4

Therefore, for p = 1 and any value of r, A cannot be equal to C.

This shows that, A is not equal to C.

Hence, for any integer

AneC

A={\(ninZ|n=2p\), for some integers p}

B={\(m inZ|m=2q-1\),for some integers q}

C={\(kinZ|k=4r\),for some integers r}

Given sets A,B,C be defined as follows

A={\(ninZ|n=2p\), for some integers p}

B={\(m inZ|m=2q-1\),for some integers q}

c={\(kinZ|k=4r\),for some integers r}

Steps:

Prove A=B

2p=2q-2

p=q-1

Given p and q are the integers.

If q is an integer, then (q-1) is also an integer.

Since, if take q = p-1 then A and B are equal.

Hence, A = B if q = p-1

Prove in the following that A = C.

n = 2p

and

k = 4r

Given, p and r are the integers.

Take p = 1 and r = 1, then

n = 2

and

k = 4

Therefore, for p = 1 and any value of r, A cannot be equal to C.

This shows that, A is not equal to C.

Hence, for any integer

AneC