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# Set Theory and Algebra MCQ - Algebra

21:

If the binary operation * is deined on a set of ordered pairs of real numbers as

(a, b) * (c, d) = (ad + bc, bd)

and is associative, then

(1, 2) * (3, 5) * (3, 4) equals

 A. (74,40) B. (32,40) C. (23,11) D. (7,11) Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
22:

If A = (1, 2, 3, 4). Let  ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is

 A. not anti-symmetric B. transitive C. reflexive D. symmetric Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
23:

Which of the following statements is false ?

 A. If R is relexive, then R ∩ R-1 ≠ φ B. R ∩ R-1 ≠ φ   =>R  is anti-symmetric. C. If R, R' are equivalence relations in a set A, then  R ∩ R'  is also an equivalence relation in A. D. If R, R' are relexive relations in A, then R - R' is reflexive Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
24:

If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3}  then R . R (= R2) is

 A. R itself B. {(1, 2),(1, 3),(3, 3)} C. {(1, 3),(2, 3),(3, 3)} D. {(2, 1),(1, 3),(2, 3)} Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
25:

A subset H of a group (G,*) is a group if

 A. a,b ∈ H=> a * b ∈ H B. a ∈ H => a-1 ∈ H C. a,b ∈ H=> a * b-1 ∈ H D. H contains the identity element Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:

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