Let #""# defined in #ZZ# by #p""q=p+q+3# for all #p,q in ZZ# Show that a) #""# is commutative in #ZZ#. b) identity element w.r.t #""# exists in #ZZ#?

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Answer 1 · 2017-04-20T22:13:28

See explanation...

a)

For all #p, q in ZZ# we find:

#p "*" q = p+q+3 = q+p+3 = q "*" p#

So #"*"# is commutative.

#color(white)()#
b)

#p "*" (-3) = p+(-3)+3 = p#

#(-3) "*" p = (-3)+p+3 = p#

So #(-3)# is an identity element with respect to #"*"#

Let #"*"# defined in #ZZ# by #p"*"q=p+q+3# for all #p,q in ZZ# Show that a) #"*"# is commutative in #ZZ#. b) identity element w.r.t #"*"# exists in #ZZ#?