Set Theory

Q41.

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

Q42.

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

Q43.

What is the cardinality of the set of integers X defined below? X=\{n \mid 1 \leq n \leq 123, n is not divisible by either 2, 3 or 5}
GateOverflow

Q44.

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
GateOverflow

Q45.

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
GateOverflow