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
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