NIMCET 2016 — Mathematics PYQ
NIMCET | Mathematics | 2016Which of the following statements is FALSE?
Choose the correct answer:
- A.
2 ∈ A ∪ B implies that 2 ∉ A then 2 ∈ B
- B.
{2, 3} ⊆ A implies that 2 ⊆ A and 3 ⊆ A
(Correct Answer) - C.
A ∩ B ⊇ {2, 3} implies that {2, 3} ⊆ A and {2, 3} ⊆ B
- D.
{2} ∈ A and {3} ∈ A implies that {2, 3} ⊆ A
{2, 3} ⊆ A implies that 2 ⊆ A and 3 ⊆ A
Explanation
Concept:
For a set A and B:
- A ∪ B is a set containing all the elements of set A and set B.
- A ∩ B is a set containing only the common elements in the set A and set B
- Subset (⊂) is the set such that all the elements of the subset are in the set from which the subset is taken from.
Calculation:
{2, 3} ⊆ A implies that 2 ⊆ A and 3 ⊆ A is false because it implies 2 ∈ A and 3 ∈ A
Explanation
Concept:
For a set A and B:
- A ∪ B is a set containing all the elements of set A and set B.
- A ∩ B is a set containing only the common elements in the set A and set B
- Subset (⊂) is the set such that all the elements of the subset are in the set from which the subset is taken from.
Calculation:
{2, 3} ⊆ A implies that 2 ⊆ A and 3 ⊆ A is false because it implies 2 ∈ A and 3 ∈ A