Question

If A = {x:x is a natural number} B = {x : x is an even natural number} C = {x : x is an odd
natural number} D = {x: x is a prime number}.
Find i) AUB ii) BUA iii) A-Biv) B-A v) What do you notice ?​

Answer 1

Step-by-step explanation:

Given:-

A = {x:x is a natural number}

B = {x : x is an even natural number}

C = {x : x is an odd natural number}

D = {x: x is a prime number}.

To find:-

Find

i) AUB

ii) BUA

iii) A-B

iv) B-A

v) What do you notice ?

Solution:-

Given sets are :

A = {x:x is a natural number}

A={1,2,3,4,5,....}--------(1)

B = {x : x is an even natural number}

B={2,4,6,8,10,....}-------(2)

C = {x : x is an odd natural number}

C={1,3,5,7,,9...}---------(3)

D = {x: x is a prime number}

D={2,3,5,7,...}----------(4)

Now,

I)AUB

={1,2,3,4,5,....} U {2,4,6,8,10,....}

AUB ={1,2,3,4,5,6,...}----------(5)

2)BUA

={2,4,6,8,10,....} U{1,2,3,4,5,....}

BUA = {1,2,3,4,5,...}----------(6)

From (5)&(6)

AUB=BUA

3)A-B

={1,2,3,4,5,....} - {2,4,6,8,10,....}

A-B ={1,3,5,7,9...}---------(7)

4)B-A

={2,4,6,8,10,....} - {1,2,3,4,5,....}

B-A = { }--------------(8)

From (7)&(8)

A -B ≠ B-A

Answer:-

1) AUB = {1,2,3,4,5,6,...}

2)BUA = {1,2,3,4,5,..}

3) A-B ={1,3,5,7,9...}

4) B -A ={ }

Observations:-

• AUB=BUA

• A -B ≠ B-A

Answer 2

Step-by-step explanation:

Given:-

A = {x:x is a natural number}

B = {x : x is an even natural number}

C = {x : x is an odd natural number}

D = {x: x is a prime number}.

To find:-

Find

i) AUB

ii) BUA

iii) A-B

iv) B-A

v) What do you notice ?

Solution:-

Given sets are :

A = {x:x is a natural number}

A={1,2,3,4,5,....}--------(1)

B = {x : x is an even natural number}

B={2,4,6,8,10,....}-------(2)

C = {x : x is an odd natural number}

C={1,3,5,7,,9...}---------(3)

D = {x: x is a prime number}

D={2,3,5,7,...}----------(4)

Now,

I)AUB

={1,2,3,4,5,....} U {2,4,6,8,10,....}

AUB ={1,2,3,4,5,6,...}----------(5)

2)BUA

={2,4,6,8,10,....} U{1,2,3,4,5,....}

BUA = {1,2,3,4,5,...}----------(6)

From (5)&(6)

AUB=BUA

3)A-B

={1,2,3,4,5,....} - {2,4,6,8,10,....}

A-B ={1,3,5,7,9...}---------(7)

4)B-A

={2,4,6,8,10,....} - {1,2,3,4,5,....}

B-A = { }--------------(8)

From (7)&(8)

A -B ≠ B-A

Answer:-

1) AUB = {1,2,3,4,5,6,...}

2)BUA = {1,2,3,4,5,..}

3) A-B ={1,3,5,7,9...}

4) B -A ={ }

Observations:-

AUB=BUA

A -B ≠ B-A