if a is equal to 15 ,b is equal to 16 and C is equal to 17 verify the following properties for addition and multiplication under closure property ,commutative property, associative property and distributive property
Answers
Given : a = 15 , b = 16 , c = 17
To find : Verification of ,commutative property, associative property and distributive property
Solution:
commutative property of addition
a + b = b + a
a = 15 b = 16
LHS = 15 + 16 = 31
RHS = 16 + 15 = 31
LHS = RHS
commutative property of multiplication
a x b = b x a
a = 15 b = 16
LHS = 15 x 16 = 240
RHS = 16 x 15 = 240
LHS = RHS
associative property of addition
(a + b ) + c = a + ( b + c)
a = 15 b = 16 c = 17
LHS = (15 + 16) + 17 = 31 +17 = 48
RHS = 15 + (16 + 17) = 15 + 33 = 48
LHS = RHS
associative property of Multiplication
(a x b ) x c = a x ( b x c)
a = 15 b = 16 c = 17
LHS = (15 x 16) x 17 = 240 x 17 = 4080
RHS = 15 x (16 x 17) = 15 x 272 = 4080
LHS = RHS
distributive property
a(b + c) = ab + ac
LHS = 15(16 + 17) = 15 x 33 = 495
RHS = 15x16 + 15x17 = 240 + 255 = 495
LHS = RHS
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