turkey-yks 2013 Q11

turkey-yks · Other · lys1-math Proof True/False Justification

Let A, B and C be sets. I. If $A \cup B = A \cup C$ then $B = C ^ { \prime }$. II. If $\mathrm { A } \cap \mathrm { B } = \varnothing$ then $\mathrm { A } \backslash \mathrm { B } = \mathrm { A } ^ { \prime }$. III. If $A \cup B = A$ then $B \backslash A = \varnothing$. Which of these propositions are always true?
A) Only I
B) Only II
C) Only III
D) I and II
E) II and III

Let A, B and C be sets.\\
I. If $A \cup B = A \cup C$ then $B = C ^ { \prime }$.\\
II. If $\mathrm { A } \cap \mathrm { B } = \varnothing$ then $\mathrm { A } \backslash \mathrm { B } = \mathrm { A } ^ { \prime }$.\\
III. If $A \cup B = A$ then $B \backslash A = \varnothing$.\\
Which of these propositions are always true?\\
A) Only I\\
B) Only II\\
C) Only III\\
D) I and II\\
E) II and III

Paper Questions

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