Equivalence Properties of Equality Tutor

Tutor is nothing but the teacher or instructor give notes to the students who comes through online. Tutor teaches a certain topic to student what they want by online. Here tutor give instruction about the equivalence property of equality to students by online. Equality represents that both side of the equation is of equal status or not. To represent this equality; we use the equivalence property of equality.

Equivalence Properties of Equality Tutor:

There are three properties under the equivalence of equality. These properties are applicable for the arithmetic operation.

Reflexive property:

Reflexive property is said to be any number that is equal to same number.

Example: a = a

Symmetric property:

Symmetric property is said to a number x is equal to the number y; then the number y is equal to the number x.

x = y then y = x

Transitive property:

Transitive Property is said to be a number an equal to the number b then the number b equal to the number c; then we can say the number an equal to the number c.

a = b; b = c and then a = c

Example Problems – Equivalence Properties of Equality Tutor:

Example 1:

Verify the following statement is transitive Property

M + 3 = 7; 7 = 4 + 3 and then 4 + 3 = 7

Solution:

Given: M + 3 = 7; 7 = 4 + 3 and then 4 + 3 = 7

Let take M + 3 = 7 ---- > equation 1

7 = 4 + 3 ---- > equation 2

4 + 3 = 7 ----- > equation 3

Step 1: Find the value of M in equation 1.

M + 3 = 7

Step 2: Subtract the number 3 on each side of the equation 1, we get

M + 3 – 3 = 7 – 3

M = 4

Thus 4 + 3 = 7 --- equation 4

That the equation 1 and equation 4 are equal,

4 + 3 = 4 + 3

Thus we proved the given statement is transitive property of equivalence.

Example 2:

Which of the following is the symmetric property?

a) m = n and n = m

b) m = 1/m and m= m

c) m + 1 = m - 1

d) m = 1 + m

Solution:

Symmetric property: x = y; y = x

Here the option ‘’a’’ refers the symmetric property.

m = n and n = m

Answer: a

These are the example problem istruct by the tutor about the equivalence properties of equality.