Last Updated on March 21, 2024 by Maged kamel

Introduction to Universal set, and subsets of sets.

What is the subset?

I quote, if every element of A is also an element of B. if whenever x ∈A, as x is a part of A, then x ∈ B, then x is an element of B.

The graph is showing A as a  small circle inside the big circle, which is  B. If all the elements in x, located at A also exist in B.

It means that A is a subset of B, this is logic. The used shapes are called Venn diagram, a diagram style that shows the logical relation between sets, the symbol used is A⊆B, A is a subset of B. Set A is included in set B.

Suppose A is intersecting with B, then A is partially part of B, but not fully. Then A is not a subset of B, to explain that, another symbol is used which is A⊄B, set A is not a subset of set B.

A Solved problem-5.

Solved problem # 5, if set A = {1,2,3,4,5,6}, while Set B={2,4,5} and set C = {1,2,3,4,5}, It is required to show the Venn diagram.

We can draw each set as circles, Set A includes numbers from A to 6, and the second circle is for B, which includes 2,4,5. While C is another circle that includes 1,2,3,4,5.

The biggest circle A is drawn first the numbers are from 1 to 6. We can select b part that includes 2,4,5 and make other shapes. We can select the C part that includes 1,2,3,4,5 as a new shape.

The only remaining part for A is number 6. A is the biggest shape, B is the smallest figure, and C is the middle shape. if we need to give an expression, we start with the smallest to the biggest.

Set B is a subset of A, and C is also a subset of A. Set B is a subset of C. If we start from the biggest 5 shapes toward the smallest shape A, the biggest shape is not a subset of B, also A is not a subset of C. C which is bigger than B is not a subset of B.

A Solved problem-6.

A Solved problem number #6, if set A={1,2,3,4}, if set B={1,4}, while set C={1}.  Describe which is the subset. Check the biggest, which is A  followed by B then C is the smallest. and also check the smallest to biggest.

For the smallest to biggest relation, B is a subset of A, since B is smaller than A. B contains 1,4 that are included in A. C is also a subset of A since element 1 is included in set A. C is a subset of B since element 1 is included in set B. But A is not a subset of B, A is >B. A is not a subset of C, A is >C.

Solved Problems-7-8.

Let us Check Solved problem #7, let set M ={a,b}, how many subsets?. What are the different alternatives? We have phi x, Ø. M has 4 substets,A={a}, B={b}, {a,b} ,Ø.

Solved problem #8, how many subsets for M. ={a,b,c}?

The answer is the following subsets are A={a}. B={b}, C={c}, later start to use the mix {a,b,c}, null, so far we have selected 5 choices. Add the alternatives {a,c},{a,b},{b,c}. We have a total of 8 subsets, all are {a},{b},{c},{a},Ø = {},{a,b,c},{a,b},{a,c}.

Universal set.

The new item is capital U is drawn as a rectangle, for any particular problem and is a set that contains all the possible elements of the problem.

A Solved Solved problem-9.

Let us have a Solved problem-9, if U={1,2,3,4,5,6,7,8,9}, while A={1,2,5,6}. While B={5,6}.

 Draw a Venn diagram to represent these sets. If we draw each set separately. This is the circle that represents A={1,2,5,6}

B={3,9}. This is the U={1,2,3,4,5,6,7,8,9}.for the Venn diagram draw the big box to represent U and draw shapes for A and B, which includes each element. For A, take {1,2,5,6} and draw a shape, then select B={3,9} and draw a shape. how many total elements that we have? we have 9 elements, already we have used 4 elements for A and 2 for B, so it is expected that the remaining are 3 elements. checking the remaining elements we will find that these elements are 4,7,8.

For an external link, math is fun for Venn diagram.
The next post, Complement of a set, Cumulative, associative, Distributive of sets.