Photo AI

Give an example of two non-empty sets A and B for which A ∩ B = A - Junior Cycle Mathematics - Question 7 - 2017

Question 7

Give an example of two non-empty sets A and B for which A ∩ B = A. Give an example of two non-empty sets P and Q for which P \ Q = P.

Worked Solution & Example Answer:Give an example of two non-empty sets A and B for which A ∩ B = A - Junior Cycle Mathematics - Question 7 - 2017

Step 1

96%

114 rated

Answer

To satisfy the condition where the intersection of sets A and B equals A, one could choose:

Let:
$A = \{1, 2, 3\}$
$B = \{1, 2, 3, 4, 5\}$

In this case, the intersection is:
$A \cap B = \{1, 2, 3\} = A$

This demonstrates that all elements of A are in B, fulfilling the requirement.

Step 2

99%

104 rated

Answer

To find sets P and Q such that the difference of P and Q equals P, they must share no common elements. For instance:

Let:
$P = \{1, 2, 3, 4\}$
$Q = \{5, 6, 7, 8\}$

Here, the difference is: $P \ Q = \{1, 2, 3, 4\}$
In this case, P is unchanged because there are no elements from Q present in P.

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;