Test: Set Theory & Algebra- 1 - Computer Science Engineering (CSE) MCQ

For S to be infinite set, atleast one of sets S_i must be infinite, since if all S_i w ere finite, then S will also be finite.

Number of elements in A x A = n² 
∴ Number of elements in the power set of
A x A = 

if a set has. n elements then its powers set has 2ⁿ elements.
Given set S = 
Number of elements in S = 3
∴ The number of elements in powerset (S)
= 2³
= 8

X and Y are sets.
The card in a lities of X and Y are |X| and |Y|  respectively.

A is a finite set with n elements. The largest equivalence relation of A is the cross-product A x A and the number of elements in the cross product A x A is n².

The number of functions from an m element set to an n element set is n^m.

The maximum number of elements in a binary relation on a set A with n elements = Number of elements in A x A = n².
Each element has two choices, either to appear on a binary relation or doesn’t appear on a binary relation.
∴ Number of binary relations = 

The empty relation on any set is always transitive and symmetric but not reflexive.

In a symmetric matrix, the lower triangle must be the mirror image of upper triangle using the diagonal as mirror. Diagonal elements may be anything. Therefore, when we are counting symmetric matrices we count how many ways are there to fill the upper triangle and diagonal elements. Since the first row has n elements, second (n - 1) elements, third row ( n - 2) elements and so on upto last row, one element. 
Total number of elements in diagonal + upper triangle

Now, each one of these elements can be either 0 or 1. So total number of ways we can fill these elements is

Since there is no choice for lower triangleelements the answer is power (2, {n² + n)/2).

Let A = { 1, 2, 3, 5, 7, 8, 9}
Construct the table for any x, y ∈ A such that