1

GATE CSE 1998

MCQ (Single Correct Answer)

+2

-0.6

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} is

2

GATE CSE 1998

Subjective

+2

-0

Let (A, *) be a semigroup. Furthermore, for every a and b in A, if $$a\, \ne \,b$$, then $$a\,*\,b \ne \,\,b\,*\,a$$.

(a) Show that for every a in A

a * a = a

(b) Show that for every a, b in A

a * b * a = a

(c) Show that for every a, b, c in A

a * b * c = a * c

3

GATE CSE 1998

Subjective

+2

-0

Suppose A = {a, b, c, d} and $${\Pi _1}$$ is the following partition of A

$${\Pi _1}\, = \,\{ \{ a,\,\,b,\,\,c\,\} \,,\,\{ d\} \,\} $$

(a) List the ordered pairs of the equivalence relations induced by $${\Pi _1}$$

(b) Draw the graph of the above equivalence relation.

4

GATE CSE 1996

MCQ (Single Correct Answer)

+2

-0.6

Let R be a non-emply relation on a collection of sets defined by $${A^R}\,B $$ if and only if $$A\, \cap \,B\, = \,\phi $$. Then, (pick the true statement)

Questions Asked from Set Theory & Algebra (Marks 2)

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