Answer the following statement(s) true (T) or false (F)

1. If a statement is true then its contrapositive must also be true.
2. If p?q and q?r then r?p.
3. The statement “if p then q” can be read as “q only if p.”
4. If a statement is false, then its converse must also be false.
5. If ?MAD = ?ROC, then ?DMA ? ?ORC.


1. True
2. False:This is the converse of the correct statement p?r.
3. False—”if p then q” is the same as “p only if q.”
4. False—A statement and it converse may or may not have the same truth value.
5. True

Mathematics

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Refer to the weighted voting system  and the Banzhaf definition of power. (The four players are P1, P2, P3 and P4.)The Banzhaf power distribution of the weighted voting system is

A. P1; P2; P3; P4.
B. P1; P2; P3; P4.
C. P1; P2; P3; P4.
D. P1; P2; P3; P4.
E. none of these

Mathematics

Perform the indicated operations. Simplify the answer. ? 

A. -16 B. 4i C. 4 D. 16i

Mathematics

Solve the problem.The number of hours of darkness in a coastal town can be modeled by , where x is the month and  corresponds to January. Approximate the number of hours of darkness in April, to the nearest tenth of an hour.

A. 17.4 hr B. 18.2 hr C. 22.7 hr D. 15.2 hr

Mathematics

Use < or > for ? to write a true sentence.  ?  

A. > B. <

Mathematics