UGAT Bangalore - Modern Math - Set Theory | Free Questions

Q1:

2025: Actual Paper

Modern Math

>

Set Theory

Medium

Let A, B and C be three sets. Then $A \cup B - C$ is not equal to

$((A - C)^c \cap (B - C)^c)^c$

$(A^c \cup C) \cup (B^c \cup C)$

$(A - C) \cup (B - C)$

$((A^c \cup C) \cap (B^c \cup C))^c$

Correct Answer

Option 2

Correct Answer

Explanation

Q2:

2025: Sample Paper

Modern Math

>

Set Theory

Medium

Let $A \times B$ denote the Cartesian product of sets $A$ and $B$ . If the cardinality of $A \cap B$ is $10$ , then the cardinality of $(A \times B) \cap (B \times A)$ is:

$2^{10}$

$10$

$100$

None of these options

Correct Answer

Option 3

Correct Answer

Explanation

Q3:

2025: Sample Paper

Modern Math

>

Set Theory

Easy

Which of the following relations is an equivalence relation?

$R_1 = \{(x,y): 3x - y = 10$ where $x$ and $y$ are real numbers $\}$

$R_2 = \{(x,y): x - y = 10$ where $x$ and $y$ are real numbers $\}$

$R_3 = \{(x,y): x - y = 0$ where $x$ and $y$ are real numbers $\}$

$R_4 = \{(x,y): x - 3y = 0$ where $x$ and $y$ are real numbers $\}$

Correct Answer

Option 3

Correct Answer

Explanation

Q4:

2025: Sample Paper

Modern Math

>

Set Theory

Easy

Let A, B, and C be three sets. Then, A-B-C is not equal to

$A \cap C^c \cap B^c$

$(A - C) - B$

$A - B \cap C$

$A - (B \cup C^c)$

Correct Answer

Option 3

Correct Answer

Explanation

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