Fsc Part 1 Mathematics (Complete Solution)

#
Q4

Show that the adjointing table represents the sums of the elements of set {E,O}.

## What is the identity element of this set? show that this set is an abelian group.

⊕ | E | O |

E | E | O |

O | O | E |

Solution:

Identity is E, the inverse of E is E and the inverse of 0 is 0.

⊕ is associative in {E,0}

As the table is symmetric about the principle diagonal therefore ⊕ is commutative.

hence {E,O} is abelian group under ⊕.