Math, asked by TbiaSupreme, 1 year ago

A is the set of prime numbers less than 10, B is the set of odd numbers < 10 and C is the set of even numbers < 10. How many of the following statements are true?
(i) A ⊂ B (ii) B ⊂ A (iii) A ⊂ C
(iv) C ⊂ A (v) B ⊂ C (vi) X ⊂ A

Answers

Answered by Acharya01
9

Given

  • A is the set of prime numbers less than 10
  • B is the set of odd numbers < 10
  • C is the set of even numbers < 10
  • set X as null set.

To find

  • the statements which are true.

Solution

we have been provided with four sets in set builder form. First let's write it in the normal form

A = {2,3,5,7}

B = {1,3,5,7,9}

C = {0,2,4,6,8}

now let's take the statement one by one,

(i) A ⊂ B

not all elements of A can be traced in Set B thus the first statement is incorrect. therefore A is not a subset of B

(ii) B ⊂ A

from the above logic it can be understood that this statement is also incorrect.

(iii) A ⊂ C

since 3 (as an example only) does not belong to set C this statement is also incorrect

(iv) C ⊂ A

since 4 does not belongs to set A this statement is also incorrect.

(v) B ⊂ C

since 3 does not belong to set C this statement is also incorrect.

set X is not described in the question, therefore we would conclude the set X to be a null set ie, a set without any elements.

(vi) X ⊂ A

since null set is a subset of every set, the statement is correct

Similar questions