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{a}in{a,b,c}...

{a}in{a,b,c}

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Prove that : |{:(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}| .

Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|

Without expanding, prove the following |(a,b-c,c-b),(a-c,b,c-a),(a-b,b-a,c)|=(a+b-c)(b+c-a)(c+a-b)

The value of |{:(a- b, b- c, c - a),(b-c,c-a,a-b),(c-a,a-b,b-c):}| =

Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

Prove: |(a+b,b+c,c+a),( b+c,c+a, a+b),( c+a, a+b,b+c)|=2|(a, b, c),( b, c, a),( c, a, b)|