Blessings I need help with proving or disproving a group of statements regarding sets / groups
A,B are groups. It is said that B = A - {1}. prove or disprove the following claims:
A. if A has the same cardinality as B then A is infinite.
B. if A!=B and if A has cardinality to B then A is infinite.
C. if A - {2} has cardinality to B then A is infinite.
Things i've already tried are
A. incorrect. counter proof : B = {} A = {} \ {1}, an empty set isn't infinite.
B.
A = {1,2,3,4,5,...} = {n|nEN}
B = {2,3,4,5,6,...} = {n|NEN}
B = A \ {1}
B != A
C. Wasn't able to anwser yet.