Question Bank - Mathematics

Here's the question bank on all the mathematics topics.

Consider the following statements in respect of two non-empty sets A and B :1. A ? B = A ? B if A = B2. A ? B = ? if A = BWhich of the above statements is/are correct ?

A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2

Solution:

Concept:1). A ? B is the symmetric difference that represents the objects that belong to A or B but not to their intersection. A ? B = (A ? B) - (A ? B)2). A ? B subset A is a subset of B. set A is included in set B.3). A ? B, ? is a union, that represents the objects that belong to set A or set B4). A ? B, ? is an intersection, that represents the objects that belong to set A and set B5). a ? A means x is an element of A, i.e. belongs to set membershipCalculation:Given that, A and B are two non-empty sets.Statement I: A ? B = A ? B if A = BLet x ? A ? x ? A ? B, [Because A ? A ? B]? x ? A ? B, [As A ? B = A ? B]? x ? A and x ? B ? x ? A,? B ? ANow, A ? B, B ? A ? A = BStatement I is correct.Statement II: A ? B = ? if A = B? A ? B = ?We know that, A ? B = (A ? B) - (A ? B)? (A ? B) - (A ? B) = ? ? (A ? B) = (A ? B)? A = BStatement II is correct.? Statement I and II both are correct.

For more questions,

Click Here

Download Gyanm App

free current affairs for competitive exams

Scan QR code to download our App for
more exam-oriented questions

free current affairs for competitive exams

OR
To get link to download app

Thank you! Your submission has been received. You will get the pdf soon. Call us if you have any question: 9117343434
Oops! Something went wrong while submitting the form.