Algebra(Quantitative Aptitude ) Questions and answers for exam Preparation

Quantitative Aptitude

ALGEBRA MCQs

Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 19 of 101 pages

Question 181. let d30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation i be a partial ordering on d30. the lub of 10 and 15 respectively is

Discuss Question

Answer: Option D. -> 30
Solution:
A partial ordering on a set is a binary relation that is reflexive, anti-symmetric, and transitive. It is also known as a preorder. The least upper bound (or supremum) of two elements in a partial order is the smallest element that is greater than or equal to both elements.
In this question, d30 is the set {1, 2, 3, 5, 6, 10, 15, 30} and i is a partial ordering on d30. The least upper bound (or supremum) of 10 and 15 is 30.
To understand why this is the case, let us consider the definition of partial ordering.
A partial ordering is a binary relation that is:
• Reflexive: for all x in the set, x ≤ x
• Anti-symmetric: if x ≤ y and y ≤ x then x = y
• Transitive: if x ≤ y and y ≤ z then x ≤ z
In the set d30, 10 and 15 are both less than or equal to 30, so 30 is the least upper bound of 10 and 15.
To illustrate this, consider the following diagram:
10 15
\ /
\ /
1 ------------ 6 --------------- 30
In this diagram, 10 and 15 are both less than or equal to 30, so 30 is the least upper bound of 10 and 15.

Question 182. let x = {2, 3, 6, 12, 24}, and ≤ be the partial order defined by x ≤ y if x divides y. number of edges in the hasse diagram of (x, ≤ ) is

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Answer: Option C. -> 4
Explanation :

Question 183. let d30 = {1, 2, 3, 4, 5, 6, 10, 15, 30} and relation i be partial ordering on d30. the all lower bounds of 10 and 15 respectively are

1,5
1,7
1,3,5
None of these

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Answer: Option A. -> 1,5
Explanation :

Question 184. hasse diagrams are drawn for

lattices
boolean Algebra
partially ordered sets
none of these

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Answer: Option D. -> none of these
Explanation :

Question 185. a self-complemented, distributive lattice is called

Self dual lattice
Complete lattice
Modular lattice
Boolean algebra

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Answer: Option D. -> Boolean algebra
Explanation :

Question 186. let d30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation i be a partial ordering on d30. the lub of 10 and 15 respectively is

Discuss Question

Answer: Option D. -> 30
Explanation :

Question 187. let d30 = {1, 2, 3, 4, 5, 6, 10, 15, 30} and relation i be partial ordering on d30. the all lower bounds of 10 and 15 respectively are