Question

Write all the proper subsets of the given set A = {x: x is a letter of the word "GOD"}

Answer 1

Answer:

X IS A LETTER OF WORD "GOD"

POSSIBLE OUTCOMES ARE 8 BUT PHI ALSO COMES BUT X IS LETTER OF WORD GOD WHEREAS PHI IS NOT LETTER DO ANSWER IS GIVEN BY2³-1

Answer 2

Concept:

One of the mathematical ideas known as Sets includes subsets. A group of items or components enclosed in curly braces, such as "a,b,c,d," is a set. A is the superset of B and B is said to be a subset of A if set A is a collection of even numbers and set B is made up of the numbers 2, 4, and 6.

Any object, including a collection of real numbers, variables, constants, whole numbers, etc., can be a set element. It also includes a null set.

Given:

A = {x: x is a letter of the word "GOD"}

Find:

Write all the proper subsets of the given set A = {x: x is a letter of the word "GOD"}

Solution:

No. of subsets= 2ⁿ

Because ∅ is included

In proper subsets,∅ is excluded

so, no. of proper subsets =2ⁿ-1

n=3

No. of proper subsets in "GOD" = 2³-1

                                                     = 7

[{G},{O},{D},{G,D},{G,O}.{O,D},{G,O,D}}

Therefore, the no. of proper subsets = 7

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