Solve the problem.Without using truth tables, show that [(p ? q) ? r] ? [r ? (~p ? ~q)].
What will be an ideal response?
| [(p ? q) ? r] ? [~r ? ~(p ? q)] | (Contrapositive) |
| ? [r ? (~(p ? q))] | (Implication) |
| ? [r ? (~p ? ~q)] | (De Morgan's law) |
Mathematics
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Find the distance between the pair of points. Where appropriate, give an approximation to three decimal places.(7, -7) and (3, -1)
A. 2
? 7.211
B. 20
? 44.721
C. 10
D. 20
Mathematics
Simplify. Assume that all variables represent any real number.
A. x
B. -x
C. 
D. -
Mathematics
Solve the problem.In a 1-mile race, the winner crosses the finish line 13 feet ahead of the second-place runner and 33 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.)
A. -13.08 ft B. 20.05 ft C. -20.13 ft D. 7.02 ft
Mathematics
Find the integral.
ln 2x dx
A. 384.91 B. -202.72 C. 391.74 D. 466.83
Mathematics