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Magazine Problem 23
With \(P=\) /all polygons/ as the universe, draw a Venn Diagram to represent the relationship between these sets. Describe a subset relationship, if one exists. Are the sets described disjoint or equivalent? Do the sets intersect? \(A=\\{\text { acute triangles }\\} ; S=\\{\text { scalene triangles }\\}\)
Problem 24
Give the indirect proof for each problem or statement. If \(x^{2} \neq 25,\) then \(x \neq 5\)
Problem 24
With \(P=\) /all polygons/ as the universe, draw a Venn Diagram to represent the relationship between these sets. Describe a subset relationship, if one exists. Are the sets described disjoint or equivalent? Do the sets intersect? \(Q=\\{\text { quadrilaterals }\\} ; L=\\{\text { equilateral polygons }\\}\)
Problem 25
With \(P=\) /all polygons/ as the universe, draw a Venn Diagram to represent the relationship between these sets. Describe a subset relationship, if one exists. Are the sets described disjoint or equivalent? Do the sets intersect? \(H=\\{\text { hexagons }\\} ; O=\\{\text { octagons }\\}\)
Problem 26
With \(P=\) /all polygons/ as the universe, draw a Venn Diagram to represent the relationship between these sets. Describe a subset relationship, if one exists. Are the sets described disjoint or equivalent? Do the sets intersect? \(T=\\{\text { triangles }\\} ; Q=\\{\text { quadrilaterals }\\}\)
Problem 26
Give the indirect proof for each problem or statement. If \(a\) and \(b\) are positive numbers, then \(\sqrt{a^{2}+b^{2}} \neq a+b\)
Problem 28
Write a formal proof of each theorem. If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
Problem 29
Give the indirect proof for each problem or statement. In a plane, if two lines are parallel to a third line, then the two lines are parallel to each other.
Problem 29
Write a formal proof of each theorem. If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary.
Problem 30
Give the indirect proof for each problem or statement. In a plane, if two lines are intersected by a transversal so that the corresponding angles are congruent, then the lines are parallel.
