how is logic different from set theory?

If A and B are two sets, we define their symmetric difference as the set of all elements that belong to A or to B, but not both A and B, and we denote it by A D B. Thu..

Introduction - In Mathematics, a well-defined collection of definite objects is called a set. George Cantor is regarded as the "Father of Set theory". The concept of "Sets" is basic in all branches of mathematics. It has proved to be of particular importance ..

The Operations on Sets are: Union of sets, Intersection of sets, Disjoint sets, Difference of two sets (Relative complement), Symmetric Difference of two sets, Complement of a set..

Question 1 - Question: For the given sequence, suggest possible next three terms and find the general term. 7, 11, 15,---- Answer: First term = 7, Common Difference = 11 - 7 = 15 - 11 = 4 Next three terms are 15 + 4 = 19, 19 + 4 = 23, 23 + 4 = ..

Difference of two sets A and B, A - B is a set whose elements belong to A but not to B. A - B is called the relative complement of B w.r.t. ..

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Induction is a principle by..

We must prove two statements. If x A and x B then, by the statement "two sets A and B are different if there exists an element which belongs to one set but not to the other" and by hypothesis, A = B is contradicted. Thus A B. Similarly B A. If A ..

Summary - (i) Let X be a set of numbers and f : N n X be a function, then the ordered set {f(1), f(2),...., f(n)} is called a finite sequence in X. (ii) Let X be a set of numbers and f : N X be a function, then the ordered set {f(1), f(2),....} is called an i..

Introduction - In Mathematics, a well-defined collection of definite objects is called a set. George Cantor is regarded as the "Father of Set theory". The concept of "Sets" is basic in all branches of mathematic..

Sets..