Related InterviewSolutions

• Let `R` and `S` be two non-void relations on a set A. Which of the following statements is false?A. R and S are transitive implies `R uu S` is transitiveB. R and S are transitive implies `R nn S` is transitiveC. R and S are symmetric implies `R uu S` is symmetricD. R and S are reflexive implies `R nn S` is reflexive
• Let A = {1, 2, 3, 4}, and let R = `{(2, 2), (3, 3), (4, 4), (1, 2)}` be a relation on A. Then, R, isA. reflexiveB. symmetricC. transitiveD. none of these
• Prove that a relation R on a set A is symmetric iff `R=R^-1`A. reflexiveB. symmetricC. transitiveD. none of these
• Let `R_(1)` be a relation defined by `R_(1)={(a,b)|agtb,a,b in R}`. Then `R_(1)` , isA. an equivalence relation on RB. reflexive, transitive but not reflexiveC. symmetric, transitive but nor reflexiveD. neither transitive nor reflexive but symmetric
• The void relation on a set A isA. reflexiveB. symmetric and transitiveC. reflexive and symmetricD. reflexive and transitive
• Let R be a reflexive relation on a set A and I be the identity relation on A. ThenA. `R sub I`B. `I sub R`C. `R = I`D. none of these
• The relation `R` defined in `N` as `aRbimpliesb` is divisible by a isA. reflexive but not symmetricB. symmetric but not transitiveC. symmetric and transitiveD. none of these
• Let R be a reflexive relation on a finite set A having n elements and let there be m ordered pairs in R, thenA. less than nB. greater than or equal to nC. less than or equals to nD. none of these
• Let R be a reflexive relation on a finite set A having n elements and let there be m ordered pairs in R, thenA. `m ge n`B. `m le n`C. `m = n`D. none of these
• Let A be a non-empty set such that `A xx A` has 9 elements among which are found (-1, 0) and (0, 1). Then,A. A = {-1, 0}B. A = {0, 1}C. A = {-1, 0, 1}D. A = {-1, 1}