Set Theory

Q41.

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Programming Language and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses. How many students have not taken any of the three courses?
GateOverflow

Q42.

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

Q43.

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