Question

A = {a,b} B = {1,2,3} Select the false statement.

a. A ∩ A² = ∅
b. (b,3) ∈ AXB
c. |A X B| = 5
d. (b, a) ∈ A²

Answer 1

The false statement is c. |A × B| = 5 because the Cartesian product of set A with 2 elements and set B with 3 elements will have 6 ordered pairs, not 5.

Step-by-step explanation:

You have provided a set A = {a,b} and a set B = {1,2,3}, and are asked to select the false statement out of the following:

• a. A ∩ A² = ∅
• b. (b,3) ∈ A×B
• c. |A × B| = 5
• d. (b, a) ∈ A²

To address each statement:

1. To evaluate statement a, we need to understand that A² usually denotes the Cartesian product of set A with itself, A×A. The intersection of a set with itself should not be the empty set unless the original set is already empty, which is not the case here. Therefore, statement a seems incorrect because A ∩ A² should not equal ∅.
2. Statement b suggests the ordered pair (b,3) is in the Cartesian product of A and B, which is true because b is in A and 3 is in B.
3. Statement c is incorrect because the size of the Cartesian product |A × B| is actually 6, since there are 2 elements in set A and 3 in set B, and multiplying these gives the number of ordered pairs in A×B.
4. Statement d is correct assuming A² means A×A, as (b, a) would indeed be an element of A².

Therefore, the false statement is c. |A × B| = 5, as the correct answer would be 6.