Brief description for post 7-discrete math.

7-Universal set Subsets of sets.

Introduction to Universal set, and subsets of sets.

Brief Description Of the Video.

The video includes the definition of Subsets of sets. The introduction to universal set and how to express it? The video has a subtitle and a closed caption in English.

You can click on any picture to enlarge and scroll for all the other images.

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.

What is the subset?

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 theVenn diagram.

We can draw each set as circles, Set A includes numbers from a to 6, 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 is 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.

Solved problem-5

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.

Solved example 6

For 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}.

Solved example -7

We have a total of 8 subsets, all are {a},{b},{c},{a},Ø = {},{a,b,c},{a,b},{a,c}.

Universal set.

What is the universal set U

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 draws the big box to represent U and draws shapes for A and B, that includes each element.

Solved example-8

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.

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