Let U = {a, b, c, d, e, f, 1, 2, 3, 4, 5, 6}, A = {a, e, 2, 4, 6}, B = {d, e, f, 3, 5, 6, 7}, C = {b, d, e, 1, 2, 3, 5, 6}. Sketch the Venn diagram of all sets. 1. List A ? B and shade the solution set. 2. List A ? B and shade the solution set. 3. List A' and shade the solution set. 4. List (A ? B)' and shade the solution set. 5. List (A ? B) ? C and shade the solution set. 6. List (A ? B) ? C' and shade the solution set. 7. Write the sample space for rolling a die and a coin simultaneously. 8. Two dice, one red and one green, are rolled. Event A is when the red die shows number 5, and event B is when the green die shows number 3. Determine the sets A ? B, A ? B, A'. 9. Find the probability of rolling two distinguishable dice and the numbers add up to 5. 10. Find the probability of rolling two distinguishable dice and get prime numbers on both dice.
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First, we need to find $A \cup B$. This is the union of sets A and B, which means we combine all the elements from both sets without repeating any elements. So, $A \cup B = \{a, e, 2, 4, 6, d, f, 3, 5, 7\}$. Show more…
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