Question

If A = {x : x is the first five multiples of 3} B; { x : x is the prime number less than 10} then find A ∪ B, A ∩ B, A − A and B − A. also represent them in venn diagram​

Answer 1

Step-by-step explanation:

Given :-

A = {x : x is the first five multiples of 3}

B = { x : x is the prime number less than 10}

To find :-

Find the following :

I) A ∪ B

ii) A ∩ B

iii) A − B

iv) B − A

v) Represent them in venn diagram ?

Solution :-

Given sets are :

A = {x : x is the first five multiples of 3}

=> A = { 3,6,9,12,15 }

B = { x : x is the prime number less than 10}

=> B = { 2,3,5,7 }

Now,

i) A ∪ B

=> { 3,6,9,12,15 } U { 2,3,5,7 }

=> { 2,3,5,6,7,9,12,15 }

Therefore, A U B = { 2,3,5,6,7,9,12,15 }

ii) A ∩ B

=> { 3,6,9,12,15 } ∩ { 2,3,5,7 }

=> { 3 }

Therefore, A ∩ B = { 3 }

iii) A - B

=> { 3,6,9,12,15 } - { 2,3,5,7 }

=> { 6,9,12,15 }

Therefore, A - B = { 6,9,12,15 }

iv) B-A

=> { 2,3,5,7 } - { 3,6,9,12,15 }

=> { 2,5,7}

Therefore, B-A = { 2,5,7}

v) See the above attachment

Answer:-

I) A U B = { 2,3,5,6,7,9,12,15 }

ii) A ∩ B = { 3 }

iii) A - B = { 6,9,12,15 }

iv) B-A = { 2,5,7}

Used formulae:-

→ AUB is the set of all elements in either A or in B or in both A and B.

→ A ∩ B is the set of all common elements in both A and B.

→ A-B is the set of all elements which belongs to A and does not belong to B.

→ B-A is the set of all elements which belongs to B and does not belong to A