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For each operation $*$ defined below, determine whether $*$ is binary, commutative or associative.(i) On $\mathbf{Z}$, define $a * b=a-b$(ii) On $\mathbf{Q}$, define $a$ * $b=a b+1$(iii) On $\mathbf{Q}$, define $a * b=\frac{a b}{2}$(iv) On $\mathbf{Z}^{+}$, define $a * b=2^{a b}$(v) On $\mathbf{Z}^{+}$, define $a$ * $b=a^{b}$(vi) On $\mathbf{R}-\{-1\}$, define $a * b=\frac{a}{b+1}$
Algebra
Chapter 1
Relations and Functions
Section 4
Composition of Functions and Invertible Function
Functions
Campbell University
McMaster University
University of Michigan - Ann Arbor
Idaho State University
Lectures
01:32
In mathematics, the absolu…
01:11
00:47
Use the commutative or the…
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00:43
Decide whether each statem…
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02:16
Perform the indicated oper…
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04:25
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Another way to find a Bool…
So we have three numbers here minus to plus three and plus six. And we need toe. Add them together in the left hand side, minus two and three. They're group together under in right hand side. Ah, unknown number along with six is added eso since minus two is taken out from the package The remaining number He is three and we are using the Assoc too. Property for edition in this case.
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