Fall 2018 COT 3100 Section 1 Homework 3 Due September29, 2018 1. What is the tru

Question

Fall 2018 COT 3100 Section 1 Homework 3 Due September29, 2018 1. What is the truth values of the following 10 12 1 divides 47 10 is divisible by 5 2. Write the following sets in roster notation Note that the above second set should read the set of x such that x divides 20. 3. Prove or disprove the following V(x, y, z e Z)((z l y) (z | z) (z | y + z)) 4. Prove or disprove the following V(x, y, z E Z)((z 1 y) ^ (z l z + y) (z 1 z)) 5. Prove or disprove the following V(x, y, z E Z)((z | y) ^ (z 1 y) (z + y l z)) 6. Prove the following (x, y, z E Z)(x )( | ()) 7. Prove the following V(x, y, z E Z)((z | y) (y | z) (z | z)) 8. Prove the following for Integers a and y 714+5y

Explanation / Answer

1. find the truth value of following

Ans: false

Reason: 10 can divide only those numbers that are multiples of 10 like 10,20,30,.......so 10 cant divides 12.

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Ans: true

Reason: 1 can divide all numbers 1,2,3,4.......................

so 1 cant divides 47. So it is true.

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Ans: true

Reason: 5 can divide only those numbers that are multiples of 5 like 5,10,15,20,. so 10 is divisible by 5. it is true.

so 10 cant divides 12.

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