College Math

College Math Study Guide

6. a Solution:

Let us solve this by making the Venn diagram.

We need to find the value of x in this case. Now we know that, a + c = 20, a + b = 19, a + d = 22, a = 10. Substituting the value of a = 10, we get; c = 10, b = 9, d = 12 We know that, (48- d – a – b) + (39 – d – a – c) + (35 – b – a – c) + a + b + c + d + x = 90 Substituting the values, we get: (48 – 12 – 10 – 9) + (39 – 12 – 10 – 10) + (35 – 9 – 10 – 10) + 10 + 9 + 10 + 12 + x = 90 17 + 7 + 6 + 41 + x = 90 x = 19 7. b Solution: Let us take each option one by one. A ∩ B denotes the intersection of A and B, the non- shaded white area in between A and B. Option C is the union of A and B, which is the shaded area plus the non-shaded white area between A and B. The fourth option denotes the total union of A and B plus the non-shaded white portion in between (the shaded portion plus twice of the white center area). The second option is the union of A and B, less the intersection of A and B; hence, option 2 is correct.

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