Question

A={c,d}

B={0,1,2}
​Select the the expression that is an element of B×A×A
A. (2,1,1)
B. (1,c,c)
C. (1,2,d)
D. (2,c,a)

Answer 1

The correct option that is an element of B×A×A is B. (1,c,c), as it properly corresponds to the elements of sets B and A.

Step-by-step explanation:

The question involves calculating the Cartesian product of the sets B and A with another A, denoted as B×A×A, which means we are looking for all possible ordered triples where the first element comes from set B, and the second and third elements come from set A. To be part of the Cartesian product B×A×A, each element in the ordered triple must correspond to the correct set. In this case, set A = {c, d} and set B = {0, 1, 2}.

We can review each option to see which one is an element of B×A×A:

• A. (2,1,1) is not correct as '1' is not an element of set A.

• B. (1,c,c) is correct as '1' is an element of set B, and both 'c's are elements of set A.

• C. (1,2,d) is not correct as '2' is not an element of set A.

• D. (2,c,a) is not correct as 'a' is not an element of set A.

Therefore, the correct option that is an element of the product B×A×A is B. (1,c,c), which I will mention as the correct option in the final answer.