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Somtimes, studying mathematics( otherwise known as scientific language) is pointless. For example, I get frustrated and exhausted when I come across a question like this: THE OPERATION * ON THE SET R OF REAL NUMBERS IS DEFINED BY A*B=(2A-1)/2 + B FOR ALL A, B BELONG TO R

1 IS THE SET R CLOSED UNDER * ?

2 IS THE OPERATION * COMMUTATIVE IN R?

3 IS THE OPERATION * ASSOCIATIVE IN R?

4 DETERMINE THE IDENTITY ELEMENT IN R

5 WHAT IS THE INVERSE OF THE ELEMENT X, IF X BELONG TO R.

Please help me solve that!

A*B = (2A-1)/2 + B ∀ A,B ∈ ℝ

(2A-1)/2 + B is real for all real values of A and B, so ℝ is closed under *.

:::::

A*B = (2A-1)/2 + B

= A - ½ + B

= B - ½ + A

= (2B-1)/2 + A

= B*A

* is commutative

:::::

(A*B)*C = [(2A-1)/2 + B]*C

= (2[(2A-1)/2 + B] - 1)/2 + C

= (2A-1 + 2B - 1)/2 + C

= A + B - 1 + C

A*(B*C) = (2A-1)/2 + (B*C)

= (2A-1)/2 + (2B-1)/2 + C

= (2A + 2B - 2)/2 + C

= A + B - 1 + C

(A*B)*C = A*(B*C)

* is associative

:::::

If I is the identity element, then A*I = A

(2A-1)/2 + I = A

I = A - (2A-1)/2

= 2A/2 - (2A-1)/2

= 1/2

:::::

I don't understand the last question.

Word Problems

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