Discrete Mathematics
Q291.
Let E,F and G be finite sets. Let X=(E \capF) - (F\capG) and Y = (E - (E\capG)) - (E - F). Which one of the following is true?Q292.
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?Q293.
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 isQ294.
Let X, Y, Z be sets of sizes x, y and z respectively. Let W=X\timesY and E be the set of all subsets of W. The number of functions from Z to E isQ297.
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}Q298.
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) isQ299.
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 toQ300.
A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?