Question

16 multiple choice 2 points
consider the statement:
the hockey game is today or tomorrow.
if we know the previous statement is false, we can conclude:
the hockey game is not today or tomorrow.
the hockey game may not be today or tomorrow.
the hockey game is not today and tomorrow.
the hockey game is the day after tomorrow.
17 multiple answer 2 points
in the diagram, \\( \overleftrightarrow { d e } \\) is a perpendicular bisector of \\( \overline { a b } \\).
which of the following statements are true? select all that apply.
\\( \overline { c d } = \overline { c e } \\)
\\( m \angle d c a = 90 ^ { \circ } \\)
\\( c \\) is the midpoint of \\( \overline { a b } \\)
\\( \overline { c e } = \overline { b c } \\)

Explanation:

Question 16

• The original statement is a logical OR statement. The negation of \(A\lor B\) (where \(A\) is "the hockey game is today" and \(B\) is "the hockey game is tomorrow") is \(

eg(A\lor B)\).

• By De - Morgan's laws, \(

eg(A\lor B)=
eg A\land
eg B\). This means the hockey game is not today and not tomorrow.

• Since \(\overleftrightarrow{DE}\) is a perpendicular bisector of \(\overline{AB}\), by the definition of a perpendicular bisector, \(C\) is the mid - point of \(\overline{AB}\) (so \(AC = CB\)) and \(\angle DCA=90^{\circ}\) (because it is a perpendicular bisector).
• There is no information given to suggest that \(CD = CE\) (we only know about the relationship with \(AB\)) and there is no reason to believe that \(CE = BC\) (since \(BC\) is related to \(AB\) and \(CE\) is related to \(DE\)).

Answer:

The hockey game is not today and tomorrow.

Question 17