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Question 1036260: Identify the properties of operations/ relations being illustrated:
a) 3∙(x∙5)=(x∙5)∙3
b) (a+b)+0=a+b
c) If a is a real number, then a + 8 is a real number
d) If a + b = c – d and c – d = e, then a + b = e.
e) √3+(-√3)=0
f) (a+b)∙(x-y)=a∙(x-y)+b∙(x-y)
g) (x+5)∙(y-3)=(y-3)∙(x+5)
h) (2r+3s)+4t=2r+(3s+4t)
i) 5=5
j) If a + 4 = b – 1, then b – 1 = a + 4.
Operations: Closure, Commutativity, associativity, identity, inverse
Relations: transitive, reflexive, symmetric
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! a) 3∙(x∙5)=(x∙5)∙3 --->Commutativity
b) (a+b)+0=a+b --->additive identity
c) If a is a real number, then a + 8 is a real number ---> Closure
d) If a + b = c – d and c – d = e, then a + b = e. ---> Transitive
e) √3+(-√3)=0 ---> additive inverse
f) (a+b)∙(x-y)=a∙(x-y)+b∙(x-y) ---> Distributivity
g) (x+5)∙(y-3)=(y-3)∙(x+5) ---> Commutativity
h) (2r+3s)+4t=2r+(3s+4t) ---> Associativity
i) 5=5 ---> Reflexive
j) If a + 4 = b – 1, then b – 1 = a + 4. --> Symmetric
Operations: Closure, Commutativity, associativity, identity, inverse
Relations: transitive, reflexive, symmetric
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