(a) If 'x' is a finite set containing 'n' elements, then prove that i…

Question

(a) If 'x' is a finite set containing 'n' elements, then prove that its power set contains $2^n$ elements.

(b) For $a/b, c/d \in \mathbb{Q}$, define a relation 'R' by $a/b \text{ R } c/d$ iff $ad = bc$. Show that R is an equivalence relation on $\mathbb{Q}$.

(c) Prove that a field is an integral domain.

Related pages

• Operations and Laws of Sets — topic
• Discrete Mathematics syllabus

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