Shade each of the following on the Venn diagrams. ( P ′ ∩ Q ) ∪ ( P ∩ Q ) (P^{\prime}\cap Q)\cup(P\cap Q)

Welcome back. For this problem, we'd like to shade P complement intersect Q, union P intersect Q on our Venn diagram. Now, this is the first time we've had two sets of parentheses, so we're just going to do them from left to right. We're gonna start here with P complement intersect Q. Now, this is the stuff in P complements, so not in P, and also in Q. So that's gonna be this region of our Venn diagram here, because it's inside of our circle for set Q, but not also inside of our circle for set P. Next, we want to deal with our second set of parentheses. So P intersect Q. We've seen this before, and we know it's just the overlap region here, inside of both our circle for P and our circle for Q, as this region represents the stuff in both P and Q. Now, if we want to take the union of these two sets, we just want to take every region that's in one or both of them. So anything highlighted in yellow and anything highlighted in blue. So we can say that P complement intersect Q, union P intersect Q, is this region, just the combination of the regions we've already highlighted, and we can see that it's actually just our circle for set Q. Now, this makes sense if we look at our two sets, because we're basically looking at the stuff in Q that's not in P and combining it with the stuff in Q that is in P. So that's just going to be everything in Q. Great work

2. Sets

Intersections and Unions

Liberal Arts Math

2. Sets

Intersections and Unions

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Multiple Choice

Shade each of the following on the Venn diagrams.
$(P^{'} \cap Q) \cup (P \cap Q)$
$Venn diagram with two overlapping circles labeled P and Q inside a rectangle labeled U, showing shaded regions for set expression.$

$Venn diagram with two circles labeled P and Q, highlighting the area of circle Q shaded in yellow.$

$Venn diagram with two sets, P shaded yellow and Q unshaded, illustrating the intersection of P and complement of Q.$

$Venn diagram with two circles labeled P and Q, shading the area representing P intersecting P intersecting Q complement.$

$Venn diagram with two circles labeled P and Q, Q circle shaded, representing set union and intersection concepts.$

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Struggling with Liberal Arts Math?

Shade each of the following on the Venn diagrams.(P′∩Q)∪(P∩Q)(P^{\(\prime\)}\(\cap\) Q)\(\cup\)(P\(\cap\) Q)

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Shade each of the following on the Venn diagrams.
$(P^{'} \cap Q) \cup (P \cap Q)$
$Venn diagram with two overlapping circles labeled P and Q inside a rectangle labeled U, showing shaded regions for set expression.$