# Important Maths Formulas for Competitive Exams pdf

Important Mathematics formula pdf for competitive exam 2020. Maths Formulas and Tricks for SSC,IBPS,UPSC and RRB exam 2020.

## Mathematics Formula PDF for competitive exam

Properties of set operations:

For any three sets A B, and C, the following hold.

(i) Commutative property

(a) A B , , = B A (set union is commutative)

(b) A B + + = B A (set intersection is commutative)

(ii) Associative property

(a) A B , , ^ h C = ^ h A B , , C (set union is associative)

(b) A B + + ^ h C = ^ h A B + + C (set intersection is associative)

(iii) Distributive property

(a) A B + , ^ h C = ^ h A B + , ( ) A C + (intersection distributes over union)

(b) A B , + ^ h C = ^ h A B , + ( ) A C , (union distributes over intersection)

Mostly we shall verify these properties with the given sets. Instead of verifying the above properties with examples, it is always better to give a mathematical proof. But this is beyond the scope of this book. However, to understand and appreciate a rigorous mathematical proof, let us take one property and give the proof.

De Morgan’s laws :

De Morgan’s father (a British national) was in the service of East India Company, India. Augustus De Morgan (1806-1871) was born in Madurai, Tamilnadu, India. His family moved to England when he was seven months old. He had his education at Trinity college, Cambridge, England. De Morgan’s laws relate the three basic set operations Union, Intersection and Complementation.