Two events $A$ and $B$ will be independent if
- A and B are mutually exclusive
- $P(A' \cap B') = (1 - P (A)) (1-P(B))$
- $P (A) = P(B) $
- $ P (A) + P(B) = 1 $
The Correct Option is B
Solution and Explanation
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Let f: ℝ → ℝ be defined as
\(f(x) = \left\{ \begin{array}{ll} [e^x] & x < 0 \\ [a e^x + [x-1]] & 0 \leq x < 1 \\ [b + [\sin(\pi x)]] & 1 \leq x < 2 \\ [[e^{-x}] - c] & x \geq 2 \\ \end{array} \right.\)
Where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t.
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Concepts Used:
Venn Diagrams
A Venn diagram can be described as a diagram that is used to represent all possible relations of distinct sets. It can be shown by any closed figure whether by a circle or a polygon. In general, circles are used to represent each set.
U reflects the universal set as a closed rectangle comprised of all the sets. The sets and subsets are shown by making use of circles or oval shapes.
Venn Diagram Symbols:
The symbols used while depicting the operations of sets are:
- Union of sets symbol: ∪
- The intersection of sets symbol: ∩
- Complement of set: A’ or Ac
