Engineering Mathematics · Sets, Relations and Functions

Official IIT answer key · IISc Bangalore · Audited Aug 2026

GATE CSE 2024 Set 1 Q32 · NAT · 1 mark

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible values of $|A|$ is ________

Numerical answer

Enter a value to check

Key concept

Sets, Relations and Functions

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Examiner trap & misconception

Topic notes

How GATE tests Sets, Relations and Functions

In this topic, GATE tests the foundational properties of finite sets, combinatorial counting of structured objects (such as matrices and function spaces), and the existence of mappings (injections, surjections, and bijections). The focus is on comparing cardinalities of constructed sets and understanding how equal or unequal cardinalities govern the existence of specific mapping types.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Engineering Mathematics · Sets, Relations and Functions

Official IIT answer key · IISc Bangalore · Audited Aug 2026

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GATE CSE 2024 Set 1 Q32 · NAT · 1 mark

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible values of $|A|$ is ________

Numerical answer

Enter a value to check

Key concept

Sets, Relations and Functions

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Sets, Relations and Functions

Full Sets, Relations and Functions guide →

More on Sets, Relations and Functions

All 5 questions on Sets, Relations and Functions →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible values of $|A|$ is ________

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Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible values of $|A|$ is ________

Step-by-step verified solution

Check you can still solve Sets, Relations and Functions under a clock

More from GATE CSE 2024 Set 1

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Let AAA and BBB be non-empty finite sets such that there exist one-to-one and onto functions (i) from AAA to BBB and (ii) from A×AA \times AA×A to A∪BA \cup BA∪B. The number of possible values of ∣A∣|A|∣A∣ is ________

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Check you can still solve Sets, Relations and Functions under a clock

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Let AAA and BBB be non-empty finite sets such that there exist one-to-one and onto functions (i) from AAA to BBB and (ii) from A×AA \times AA×A to A∪BA \cup BA∪B. The number of possible values of ∣A∣|A|∣A∣ is ________

Step-by-step verified solution

Check you can still solve Sets, Relations and Functions under a clock

More from GATE CSE 2024 Set 1

More on Sets, Relations and Functions

Share this solution

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible values of $|A|$ is ________

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible values of $|A|$ is ________