1
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
2
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.
3
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.
4
GATE CSE 2019
MCQ (Single Correct Answer)
+2
-0.67
Consider the first order predicate formula φ:

∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))]

Here 'a|b' denotes that 'a divides b', where a and b are integers.

Consider the following sets:

S1. {1, 2, 3, ..., 100}
S2. Set of all positive integers
S3. Set of all integers

Which of the above sets satisfy φ?
A
S1 and S3
B
S1, S2 and S3
C
S2 and S3
D
S1 and S2
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