Question

directions: draw a venn - diagram to represent each statement. 1. trapezoids are never parallelograms. 2. every apple is a fruit. 3. all linear pairs are supplementary angles. 4. some teens who babysit also mow lawns. directions: shade the indicated region of the venn diagrams below. 5. p 6. p ∧ q 7. p ∨ q 8. ¬p ∧ q 9. (q ∨ r) ∧ ¬p 10. (¬q ∧ p) ∨ r directions: write a logic statement to represent the shaded region. 11. 12. 13. 14. some students who take band also take art. if jack takes art but not band, shade the area on the diagram where he would belong.

Explanation:

Step1: Draw Venn - diagrams for statements 1 - 4

1. For "Trapezoids are never parallelograms", draw two non - overlapping circles, one for trapezoids and one for parallelograms.
2. For "Every apple is a fruit", draw a small circle for apples inside a larger circle for fruits.
3. For "All linear pairs are supplementary angles", draw a small circle for linear pairs inside a larger circle for supplementary angles.
4. For "Some teens who babysit also mow lawns", draw two overlapping circles, one for teens who babysit and one for teens who mow lawns.

Step2: Shade Venn - diagrams for statements 5 - 10

1. For \(p\), shade the entire circle labeled \(p\).
2. For \(p\land q\), shade the overlapping region of circles \(p\) and \(q\).
3. For \(p\lor q\), shade the region that includes all of circle \(p\) and all of circle \(q\) (including the overlap).
4. For \(

eg p\land q\), shade the non - overlapping part of circle \(q\) with circle \(p\) (the part of \(q\) outside \(p\)).

1. For \((q\lor r)\land

eg p\), first find \(q\lor r\) (shade all of \(q\) and \(r\) including the overlap), then find the part of that region that is outside \(p\).

1. For \((

eg q\land p)\lor r\), first find \(
eg q\land p\) (shade the part of \(p\) outside \(q\)), then combine it with circle \(r\) (shade all of \(r\) and the previously shaded part of \(p\)).

Step3: Write logic statements for statements 11 - 13

1. The shaded region represents \((p\land

eg q)\lor r\).

1. The shaded region represents \(q\land r\land

eg p\).

1. The shaded region represents \((p\land q\land r)\lor(q\land r\land

eg p)\).

Step4: Shade for statement 14

For "Some students who take band also take art" with Jack taking art but not band, shade the non - overlapping part of the Art circle with the Band circle.

Answer:

Venn - diagrams are drawn and shaded as described above, and logic statements are written as described above.