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Problem 1

# Let $$S=\\{a, b, c, d, e, f\\}$$ be a sample space of an experiment and let $$E=\\{a, b\\}, F=\\{a, d, f\\}$$, and $$G=\\{b, c, e\\}$$ be events of this experiment. Find the events $$E \cup F$$ and $$E \cap F$$.

Expert verified
E ∪ F = {a, b, d, f} and E ∩ F = {a}
See the step by step solution

## Step 1: Identify the Given Sets

We are given the following sets: Sample space S = {a, b, c, d, e, f} Event E = {a, b} Event F = {a, d, f} Event G = {b, c, e}

## Step 2: Find the Union of E and F (E ∪ F)

To find E ∪ F, we will combine all the unique elements from events E and F. E ∪ F = {a, b} ∪ {a, d, f} = {a, b, d, f}

## Step 3: Find the Intersection of E and F (E ∩ F)

To find E ∩ F, we will look for the elements that are common to both events E and F. E ∩ F = {a, b} ∩ {a, d, f} = {a} The events E ∪ F and E ∩ F are therefore {a, b, d, f} and {a} respectively.

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