Statement (I): If H is a non-empty finite subset of a group G and ab ∈ H for all a, b ∈ H, then H is also a group.
Statement (II): There is no homomorphism from (Z, +) to (Q, +), where Z is the set of integers and Q the set of rationals.
In the light of the above statements, choose the most appropriate answer from the options given below:
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: C. Statement I is correct but Statement II is incorrect
Explanation
A finite non-empty subset closed under the operation is a subgroup (I true). The inclusion map n ↦ n (or the zero map) is a homomorphism from (Z, +) to (Q, +), so II is false.More Discrete Structures and Optimization questions
- The cost function of the total food is:
- Which of the following are the constraints when formulating the LPP?
- What are the quantities (in grams) of food X and Y respectively when the cost of food is minimum?
- The dual of the formulated LPP is:
- The minimum cost of food is:
- Consider the universe of positive integers X = {n | 1 ≤ n ≤ 8}, proposition P = "n is an even integer", Q = "(3 ≤ n ≤ 7) ∧ (n ≠ 6)". The tr…