## Question

###### Homework 5 Complete each of the following problems Be sure to include any relevant work and explanation. 1. (2 points) Prove by induction that the following equation holds for every positive integer n: Zk? = nlnt WZn+1 k=] 2 Let M(xy) denote "x Has emailed y", T(xy) denote has textedy", and P(xy) denote "x has called Iy on the phone' where tne the Cartesian product of the set of students in this class with itself: Translate the following into clear English sentence: Vvax

Homework 5 Complete each of the following problems Be sure to include any relevant work and explanation. 1. (2 points) Prove by induction that the following equation holds for every positive integer n: Zk? = nlnt WZn+1 k=] 2 Let M(xy) denote "x Has emailed y", T(xy) denote has textedy", and P(xy) denote "x has called Iy on the phone' where tne the Cartesian product of the set of students in this class with itself: Translate the following into clear English sentence: Vvax(M(x v)v Tlx V)v Ax,v)) b. Use the given propositiona functions, quantifiers, and any other necessary logical operators to express the following stateme spoken on the phone: 3. (2 points) Prove by induction that the sequence of the positive powers of 3 Is increasing: Homework 6 Meraitatel NAtt