Question

What is the definition of refelxive, symmetric,transitive,associative,commutative and distributive properties. Examples would be very helpful.

Answer 1

The reflexive property:
a=a

For example, 3 = 3

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The symmetric property:
If a=b, then b=a

For example, x = 3 implies that 3 = x

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The transitive property:
If a=b and b=c, then a=c

For example, if x = 3 and 3 = y, then x=y

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The associative property:
(a + b) + c = a + (b + c) and (a*b)*c = a*(b*c)

For example:
(1+2)+3 = 3 + 3 = 6 = 1+5 = 1+(2+3)
(2*3)*4 = 6*4 = 24 = 2*12=2*(3*4)

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The commutative property:
a + b = b+ a and a*b = b*a

For example:
3+4 = 7 = 4+3
2*3 = 6 = 3*2

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The distributive property:
a*(b+c) = a*b + a*c

For example:
3*(4+5) = 3*9 = 27 = 12 + 15 = 3*4 + 3*5

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Hope this helps! If you have any questions, feel free to ask

Answer 2

Thanks a bunch!