Question

Let A={2,3,4} B={2,5,6} C={5,6,2} and D={6}. Determine if the following statements are true:

i). 4€C
ii). 5€C
iii). A=B
iv). B=C​

Answer 1

i. 4∈C => False

ii. 5∈C => True

iii. A = B => False

iv. B=C => True

Explanation:

Given sets are:

`A = \{2,3,4\}\\B = \{2,5,6\}\\C = \{5,6,2\}\\D = \{6\}`

Lets look at the statements one by one.

i. 4∈C

This statement means that 4 is a member of set C. Looking at the members of set C, it can be concluded that the statement is wrong as C doesn't contain 4.

ii. 5∈C

This statement is true as 5 is a member of C.

iii. A=B

This statement states that set A is equal to set B. Two sets are said to be equal if there number of elements and members are same. Set A and Set B have different members so this statement is false.

iv. B=C

Set B and Set C have equal number of members and the members (5,6,2) are also same so the statement is true.

Hence,

i. 4∈C => False

ii. 5∈C => True

iii. A = B => False

iv. B=C => True