Question

The sum of any two numbers and the sum obtained by changing the order of those numbers is the same: How is this statement written using letters for number? 11a + b = x+y (2) a + b = b + a (3) a x b = bx a (4) a = b = b + a​

Answer 1

Answer:

if a & b are two non- empty subsets and we have to prove axb=bxa iff a=bproof:we will prove this in two parts. in first part we will prove that if a=b then axb=bxa and in the second part we will prove that if axb=bxa then a=b.i) for the first part let us assume that a=bthen in axb we can first replace first ‘a’ with ‘b’ (as by assumption a=b) so that it becomes bxb. now we have axb=bxb. in the next step we replace ‘b’ with ‘a’ so that bxb can be written as bxa.thus we have axb=bxb=bxaii)for the second part we assume that axb=bxa and then we will prove that a=b. we will prove this by double containment. we will prove that a is subset of b and then b is subset of a .let x∈ a and y∈bnow (x, y) ∈ axbbut by our assumption axb and bxa are equalso (x,y) ∈ bxa implying that x ∈b , sine x is an arbitrarily chosen element, so a is subset of b.now let x∈b and y∈aso (x,y) ∈ bxabut again since bxa=axb; therefore x∈a. thus implying as before that bis subset of athus from double containment viz. a being subset of b and b being subset of a; we get a=b.

Step-by-step explanation: