Search & Filtering
Show that if A, B, and C are sets, then A ∩ B ∩ C = A ∪ B ∪ C
by showing each side is a subset of the other side.
using a membership table.
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find
A ∩ B ∩ C.
A ∪ B ∪ C.
(A ∪ B) ∩ C.
(A ∩ B) ∪ C.
if R={(1,2),(2,1),(3,1),(2,3)} be a relation defined on A={1,2,3)then transitive closure of R is
Show that if any five numbers from 1 to 8 are chosen, then two of them will add up to 9.
an=3an−1+n2−3,n≥,a0=1
There are three kinds of people on an island: knights who always tell the truth, knaves who always lie, and spies who can either lie or tell the truth. You encounter three people, A, B, and C. You know one of these people is a knight, one is a knave, and one is a spy. Each of the three people knows the type of person each of other two is. A says “I am the knight,” B says “A is not the knave,” and C says “B is not the knave". Is there a unique solution to determine the knight, the knave, and the spy? If yes, determine who the knight, knave, and spy are.
Let R br a realtion defined from the set A={1,2,3,4} to the set B={2,3,4,5}as a€A, b€B aRb <-> a+b=5
1. What are the orderd pairs in the relation R
2. Represent R with a matrix
What is mean by logic
Solve the following set of recurrence relations and initial conditions3an-1+n^2-3,n>1,a0=1
1. There are 41 candidates approved to be allotted as the F.D.R.E. council of cabinets. Historic facts of the candidates are shown below, 8 were served as former cabinet members,14 were university presidents, 15 served as members of P.R.H., 2 served in former cabinet and as P.R.H, 4 served as university presidents and members of former cabinet, 6 were served as university presidents and members of P.R.H, 1 served in all the three positions. The find the number of candidates:
a. Served in none of the three positions?
b. Only university presidents?
c. At least one of the three positions?
d. Exactly two positions?
