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content/exercises/graded-assignments/mathematics-1/W1GA1.md

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@@ -81,6 +81,7 @@ Number who watched Avatar and RRR $N(A \cup R) = 40$
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Number who watched Dabang and RRR $N(D \cup R) = 55$
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Let $x$ be the number who watched all three movies.
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**Solution:**
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$$
@@ -92,6 +93,7 @@ x + 150 = 180 \implies x = 30
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$$
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Number who watched only RRR and Avatar = $40 - x = 10$
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@@ -116,10 +118,15 @@ Let $R_2 = \{(x,y) \mid x, y \in S, y = x^2\}$
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Find the cardinality of $R_1 \setminus (R_1 \cap R_2)$.
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**Solution:**
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$S = \{0,1,2,\ldots,18\}$
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$R_1 = \{(0,0),(1,3),(2,6),(3,9),(4,12),(5,15),(6,18)\}$
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$R_2 = \{(0,0),(1,1),(2,4),(3,9),(4,16)\}$
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$R_1 \cap R_2 = \{(0,0),(3,9)\}$
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$R_1 \setminus (R_1 \cap R_2) = \{(1,3),(2,6),(4,12),(5,15),(6,18)\}$
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**Answer:** 5

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