GATE CSE 1996 | Set Theory & Algebra Question 93 | Discrete Mathematics

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)

R is reflexive and transitive

R is symmetric and not transitive

R is an equivalence relation

R is not reflexive and not symmetric

GATE CSE 1995

MCQ (Single Correct Answer)

-0.6

Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Then

A is closed under * but $$ < A,\,* > $$ is not a semigroup.

$$ < A,\,* > $$ is a semigroup but not a monoid.

$$ < A,\,* > $$ is a monoid but not a group.

$$ < A,\,* > $$ is a group but not an abelian group

GATE CSE 1994

MCQ (Single Correct Answer)

-0.6

Some group (G, o) is known to be abelian. Then, which one of the following is true for G?

$$g = {g^{ - 1}}\,$$ for every $$g\, \in \,G$$.

$$g = {g^{ 2}}\,$$ for every $$g\, \in \,G$$.

$${(goh)^2} = \,{g^2}\,o\,\,{h^2}$$ for every g, $$h\, \in \,G$$.

G is of finite order.

GATE CSE 1989

Fill in the Blanks

-0

The transitive closure of the relation
$$\left\{ {\left( {1,2} \right)\left( {2,3} \right)\left( {3,4} \right)\left( {5,4} \right)} \right\}$$
on the set $$A = \left\{ {1,2,3,4,5} \right\}$$ is ________ .

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