Discrete Mathematics–Important Points for Review

Some important points / Questions in +2 Discrete Mathematics from an SSLC examination angle.

1) N = set of all Natural numbers = { 1,2,3,……..}

2) W = set of all whole numbers = {0,1,2,3,……}

3) Z = set of integers = {0,+1,-1,+2,-2,…….}

4) Z+ = N

5) Q = the set of all rationals

6) Q* = the set of all non zero rationals

7) R = the set of all reals

8) R* = the set of all non zero reals

9) R+ = the set of all positive reals

10) C = the set of all complex numbers

11) C+ = the set of all non zero complex numbers

12) Closure Axiom : Binary operation on G is a map from G x G into G. If * is a binary operation then

$\forall \; a, b \; \epsilon \; G, a * b \; \epsilon \; G$

This axiom can also be called as the closure property of G w.r.t. *.

13) Associative Axiom: $(a*b)*c=a*(b*c)\; \forall \; a,b,c \; \epsilon \; G$

14) Identity Axiom: If there exists an element of the form $e \; \epsilon \; G$ such that $a*e=e*a \; \forall \; a \; \epsilon \; G$ then e is called the identity.

15) Commutative Axiom: * is commutative if $a*b=b*a \; \forall \; a,b \; \epsilon \; G$