Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L G and that the size of L is at least 4. The size of L is …

Official answer: 5. Explanation: By Lagrange's Theorem, the order (size) of any subgroup L of a finite group G must divide the order of G. Given: - |G| = 15 - The divisors of 15 are 1, 3, 5, and 15. We are given the following conditions on |L|: 1. L is a proper subgroup (L G), so |L| < 15. 2. The size of L is at least 4, so |L| 4. The only divisor of 15 strictly less than 15 and greater than or equal to 4 is 5. Therefore, the size of L is 5.

Engineering Mathematics · Sets, Relations, Lattices and Groups

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 3 Q3 · NAT · 1 mark

Let $G$ be a group with 15 elements. Let $L$ be a subgroup of $G$ . It is known that $L \neq G$ and that the size of $L$ is at least 4. The size of $L$ is _______.

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Sets, Relations, Lattices and Groups

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How GATE tests Sets, Relations, Lattices and Groups

In GATE CS, questions on sets, relations, and functions test formal mathematical rigor through algebraic verification of binary relation properties (reflexivity, symmetry, transitivity), set-theoretic properties of direct and inverse images of functions, and state-reachability or partition analysis on integer domain functions. The questions range from conceptual 1-mark MCQs on standard definitions and counterexamples to 2-mark algebraic or NAT problem-solving items involving equivalence classes and modular cycles.

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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, Lattices and Groups

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

Take topic test

GATE CSE 2014 Set 3 Q3 · NAT · 1 mark

Let $G$ be a group with 15 elements. Let $L$ be a subgroup of $G$ . It is known that $L \neq G$ and that the size of $L$ is at least 4. The size of $L$ is _______.

Numerical answer

Enter a value to check

Key concept

Sets, Relations, Lattices and Groups

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Sets, Relations, Lattices and Groups

Full Sets, Relations, Lattices and Groups guide →

More on Sets, Relations, Lattices and Groups

All 11 questions on Sets, Relations, Lattices and Groups →

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

Let $G$ be a group with 15 elements. Let $L$ be a subgroup of $G$ . It is known that $L \neq G$ and that the size of $L$ is at least 4. The size of $L$ is _______.

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Let $G$ be a group with 15 elements. Let $L$ be a subgroup of $G$ . It is known that $L \neq G$ and that the size of $L$ is at least 4. The size of $L$ is _______.

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

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Let GGG be a group with 15 elements. Let LLL be a subgroup of GGG. It is known that L≠GL \neq GL=G and that the size of LLL is at least 4. The size of LLL is _______.

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Let GGG be a group with 15 elements. Let LLL be a subgroup of GGG. It is known that L≠GL \neq GL=G and that the size of LLL is at least 4. The size of LLL is _______.

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

More from GATE CSE 2014 Set 3

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Let $G$ be a group with 15 elements. Let $L$ be a subgroup of $G$ . It is known that $L \neq G$ and that the size of $L$ is at least 4. The size of $L$ is _______.

Let $G$ be a group with 15 elements. Let $L$ be a subgroup of $G$ . It is known that $L \neq G$ and that the size of $L$ is at least 4. The size of $L$ is _______.