COMEDK · Maths · 17. Mathematical Reasoning
Which of the following is false?
- A Addition is commutative in \(N\).
- B Multiplication is associative in \(N\).
- C If \(a * b=a^{b}\) for all \(a, b \in N\), then \(*\) is commutative in \(N\).
- D Addition is associative in \(N\).
Answer & Solution
Correct Answer
(C) If \(a * b=a^{b}\) for all \(a, b \in N\), then \(*\) is commutative in \(N\).
Step-by-step Solution
Detailed explanation
\(a*b=a^{b}\) and \(b * a=b^{a}\) \[ \therefore \quad a * b \neq b \neq a ; \forall a, b \in N \] So, addition is commutative in \(N\). (b) \((a \times b) \times c=a \times(b \times c), \forall a, b, c \in N\). So, multiplication is associative in \(N\). (c) \(a*b=a^{b}\) and…
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