Definition of Subset Learning

We come across set of different kinds in everyday life. A football team is set of players, a class is a set of students, a set of books in mathematics and so on. Basically, the set is an undefined term.  Anyhow, it can be a well defined  collection of objects. Here the word 'objects' has been taken in wider and broader sense. Mathematically, the numbers, words, letters, signs, symbols, thoughts, etc. all are the objects. Let us learn about a set and  definition of a subset in this article.

Learning Definition of a Subset

Definition

If each element of A is an element of B, then the set A is said to be a sub set of the set B.

Symbolically, we represent this by A `sub` B and read it as ' A is a subset of B'.

Thus A `sub` B `hArr` (  x `in` A   `rArr` x `in` B ).

If A `sub` B and A `!=` B then the set A is said to a proper subset of B.

learning examples of subset

1. {1, 2, 3, 4, 5 } `sub` { x : x is a natural number }

2. { a, b, c, d } `sub` { a, b, c, d, e}

3. Set of all vowels is a subset of set of all alphabets

4. A = { set of all integers}

B = { set of all positive integers}

B is a subset of A.

5. T = { x : x is a student of class 9 in your school }

W = { x : x is a student in your school}

T is a subset of W.



Definition of Subset Learning - Points to Remember

1. `phi` `sub` A ( since `phi` has no elements, it is a subset of every set)

2. A `sube` A ( every set is a subset of itself)

3. A `sube` B and B `sube` A `hArr`    A = B

4. A `sub` B and B `sub` D `=>`   A `sub` D

5. If A `sub` B, then x `!in` B `rArr` x `!in` A.

Adding Exponents Worksheet

Exponents are nothing but multiplying the number by itself.  For example, y2 is the same as y * y. Exponent denotes the number of times the number needed to be multiplied by itself. An exponent is nothing but a superscript, or small number that can be written at the top right edge of a number, variable, or set of parentheses. In this article we shall discuss the adding exponents worksheet.

Problems for Adding Exponents Worksheet:

Adding exponents worksheet:

Problem 1:

To find x3y4. x5y3

Solution:

Rearrange the factors and multiply the exponent terms, using the rule

Here,

am.an = am+n

= (x3. x5)( y3. y4)

= x8. Y7

X and y are different terms,

So the final result is x8. Y7

Problem 2 for Adding exponents worksheet:

To find  (32)3

Solution:

(32)3 = 93 =  729 using power rule,

The answer is 729

Problem 3:

To find  (22)3

Solution:

(22)3 =(2x2)3 =  43=64 using power rule,

The answer is 64

Mixed variables for multiply exponents worksheet:

Have a mix of variables:

Example 1:

=xy2z y3z

=x y2+3z1+1

=xy5z2

so the result is =x3y5z2

Example 2:

=x3y3z3 .  x2yz

=x3+2 y3+1 z3+1

=x5y4z4

so the result is =x5y4z4

With constant examples:

Example 1:

=5xyz .4xyz

=(5 4)x1+1 y1+1 z1+1

=20x2y2z2

The result is =20x2y2z2

Example 2:

=7xyz.3 x2yz

=(73 ) x1+2y1+1z1+1

=21x3 y2z2

The result is  =21x3 y2z2
More Examples for Multiply Exponents Worksheet:

Example 1:

=5xyz `xx` 4xyz

= (5`*` 5)x1+1 y1+1 z1+1

=25x2y2z2

The result is =25x2y2z2

Example 2:

=7xyz `xx` 4 x2yz

= (7`*` 4) x1+2y1+1z1+1

=28x3 y2z2

The result is  =28x3 y2z2

Example 3:

=5xyz `xx` 7xyz

=(7`*` 5)x1+1 y1+1 z1+1

=35x2y2z2

The result is =35x2y2z2

Example 4:

=7xyz  ` xx` 2 x2yz

= (7`*` 2 ) x1+2y1+1z1+1

=14x3 y2z2

The result is  =14x3 y2z2