2.22 Prove or disprove the following conjectures. (a) There is an even integer w

Question

2.22 Prove or disprove the following conjectures. (a) There is an even integer which can be expressed as the sum of three even integers. b) Every even integer can be expressed as the sum of three even integers. (c) There is an odd integer which can be expressed as the sum of two odd integers. (d) Every odd integer can be expressed as the sum of three odd integers. To get a feel about whether a claim is true or false, try out some examples. If you believe a claim is false, provide a specific counterexample. If you believe a claim is true, give a (formal) proof

Explanation / Answer

a) True

sum of three even number is always even number

example : 8 = 2+4+2

b) False :

4= 2+2 no 3rd even number i.e not possible to write sum of three even number

c) False :

sum of two odd is always an even number .

e.g. 1+3=4 9+5=14  

d) True:

sum of three odd integer is always add

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