Relation
Q11.
Let L be a set with a relation R which is transitive, anti-symmetric and reflexive and for any two elements a, b \in L, let the least upper bound lub (a, b) and the greatest lower bound glb (a, b) exist. Which of the following is/are true?Q13.
The binary relation R = \{(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)\} on the set A=\{1, 2, 3, 4\} isQ15.
Let R be a non-empty relation on a collection of sets defined by _{A}R_ B if and only if A \cap B = \phi. Then, (pick the true statement)Q16.
Suppose A is a finite set with n elements. The number of elements in the largest equivalence relation of A isQ17.
Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}. Which one of the following is TRUE?Q18.
A relation R is defined on the set of integers as xRy iff (x + y) is even. Which of the following statements is true?Q20.
Consider the following relations: R1(a,b) iff (a+b) is even over the set of integers R2(a,b) iff (a+b) is odd over the set of integers R3(a,b) iff a.b > 0 over the set of non-zero rational numbers R4(a,b) iff |a - b| <= 2 over the set of natural numbers Which of the following statements is correct?