1
GATE CSE 2024 Set 2
Numerical
+2
-0.66

Let Zn be the group of integers {0, 1, 2, ..., n − 1} with addition modulo n as the group operation. The number of elements in the group Z2 × Z3 × Z4 that are their own inverses is __________.

Your input ____
2
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+2
-0.66
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?
A
Operator $\diamond$ obeys the associative law
B
Operator $\square$ obeys the associative law
C
Operator $\triangle$ over the operator $\square$ obeys the distributive law
D
Operator $\square$ over the operator $\Delta$ obeys the distributive law
3
GATE CSE 2023
MCQ (More than One Correct Answer)
+2
-0.67

Let X be a set and 2$$^X$$ denote the powerset of X. Define a binary operation $$\Delta$$ on 2$$^X$$ as follows:

$$A\Delta B=(A-B)\cup(B-A)$$.

Let $$H=(2^X,\Delta)$$. Which of the following statements about H is/are correct?

A
H is a group.
B
Every element in H has an inverse, but H is NOT a group.
C
For every $$A\in2^X$$, the inverse of A is the complement of A.
D
For every $$A\in2^X$$, the inverse of A is A.
4
GATE CSE 2021 Set 1
MCQ (More than One Correct Answer)
+2
-0.67
A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?
A
If a relation S is transitive and circular, then S is an equivalence relation.
B
If a relation S is reflexive and symmetric, then S is an equivalence relation.
C
if a relation S is reflexive and circular, then S is an equivalence relation.
D
if a relation S is circular and symmetric, then S is an equivalence relation.
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