Set Theory Practice Questions

Let P(S) denotes the power set of set S. Which of the following is always true?

Given $\Sigma=\{a,b\}$ , which one of the following sets is not countable?

A partial order $\leq$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \} \text{ as }x \leq _{i} a_{i}$ for all $i$ and $a_{i}\leq y$ for all i, where $n \geq 1$ . The number of total orders on the set S which contain the partial order $\leq$ is

Let A and B be sets and let $A^c$ and $B^c$ denote the complements of the sets A and B. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to

Let $X = \{2, 3, 6, 12, 24\}$ , Let $\leq$ be the partial order defined by $X \leq Y$ if x divides y. Number of edges in the Hasse diagram of $(X, \leq)$ is

The number of elements in the power set P(S) of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is:

Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is:

Let S be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$ . Then

Consider the set of integers {1,2,3,4,6,8,12,24} together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?