Sets Formula - Theory, Properties, Solved Examples

Sets Formula: Set formulas encompass the mathematical expressions pertinent to set theory. A set denotes a gathering of precisely defined items, each possessing unique attributes. Familiarity with sets equips us to employ set formulas across domains such as statistics, probability, geometry, and sequences.

Also Check - Comparing Quantities Formula

Important Sets used in Mathematics

• N: It consists of Set of all natural numbers = {1, 2, 3, 4, …..}
• Q: Set of all rational numbers
• R: Set of all real numbers
• W: Set of all whole numbers
• Z: It contains Set of all integers = {….., -3, -2, -1, 0, 1, 2, 3, …..}
• Z+: Set of all positive integers

Also Check - Congruence of Triangles

What are the Various Types of Sets?

(A) n(A) n(A) n(A) n(A) (B),

Also Check - Cubes and Cubes Roots Formula

Three Approaches to Representing Sets

2 = 2 x 1

4 = 2 x 2

6 = 2 x 3

8 = 2 x 4

Also Check - Factorization Formula

What Are the Sets Formulas?

Sets Formulas on Properties of Sets

Sets Formulas of Complement Sets

Sets Formulas of Difference of Sets

• A - A = Ø
• B - A = B⋂ A'
• B - A = B - (A⋂B)
• (A - B) = A if A⋂B = Ø
• (A - B) ⋂ C = (A⋂ C) - (B⋂C)
• A ΔB = (A-B) U (B- A)
• n(AUB) = n(A - B) + n(B - A) + n(A⋂B)
• n(A - B) = n(A∪B) - n(B)
• n(A - B) = n(A) - n(A⋂B)
• n(A') = n(U) - n(A)

Other Important Sets Formulas

• n(U) = n(A) + n(B) + - n(A⋂B) + n((A∪B)')
• n((A∪B)') = n(U) + n(A⋂B) - n(A) - n(B)