Consider the following five relations on the set A = { 1, 2, 3, 4 } : R1 = { (1, 1), (1, 2), (2, 3), (1, 3), (4, 4) }
R2 = { (1, 1)(1, 2), (2, 1), (2, 2), (3, 3), (4, 4) }
R3 = { (1, 3), (2, 1) }
R4 = ∅ , the empty relation
R5 = A × A, the universal relation

Fill in the following table cells with “yes” or “no” if the relation R1-R5 has the said property.

Geometry: determine whether segment mn is parallel to segment kl. justify your answer. jm 6 mk 3 jn 8 nl 4

Find the slope of the line that contains the following points. r(-2, 4), s(6, -2)

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.