If-two-sets-A-and-B-are-having-99-elements-in-common-then-the-number-of-elements-common-to-each-of-the-sets-A-B-and-B-A-is-

Question Number 114233 by Aina Samuel Temidayo last updated on 18/Sep/20

If two sets A and B are having 99

elements in common, then the

number of elements common to each

of the sets A \times B and B \times A is

Answered by 1549442205PVT last updated on 20/Sep/20

A = {x_{1}, x_{2}, \dots, x_{m}, c_{1}, c_{2}, \dots, c_{99}}

B = {y_{1}, y_{2}, \dots, y_{n}, c_{1}, c_{2}, \dots, c_{99}}

\Rightarrow A \times B and B \times A {haveF}_{99}^{2} = 99^{2}

= 9801 common elements because

the common elements are

{(c_{i}, c_{j}) (1 ⩽ i, j ⩽ 99)}

Commented by 1549442205PVT last updated on 18/Sep/20

Thank you . I corrected . You just need

instead of 99 by 4 and check

Commented by Aina Samuel Temidayo last updated on 18/Sep/20

Not correct .

Commented by 1549442205PVT last updated on 20/Sep/20

It is F_{99}^{2} . Note F_{n}^{k} = n^{k} . Note that

Given two sets A = {x_{i}}_{i = 1}^{m}, B = {y_{j}}_{j = 1}^{n}

Then A \times B = {(x_{i}, y_{j}) ∣ 1 ⩽ i ⩽ m, 1 ⩽ j ⩽ n}

B \times A = {(y_{i}, x_{j}) ∣ 1 ⩽ i ⩽ n, 1 ⩽ j ⩽ m}