Discrete Mathematics
Q291.
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 isQ293.
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 n = p^{2}q, where p and q are distinct prime numbers. How many numbers m satisfy 1 \leq m \leq n and gcd(m,n)=1? Note that gcd(m,n) is the greatest common divisor of m and n.Q295.
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?Q296.
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?