# Answer the True or False Questions Based on Algebra

# True or False

- True or false. A set is any collection of objects.
- True or false. A proper subset of a set is itself a subset of the set, but not vice versa.
- True or false. The empty set is a subset of every set.
- True or false. If ;
*A*;∪ ;*B*;= ;∅ , then ;*A*;= ; ∅ ;and ;*B*;= ; ∅ ;. - True or false. If ;
*A*;∩ ;*B*;= ; ∅ ;, then ;*A*;= ; ∅ ;or ;*B*;= ; ∅ ;or both*A*;and ;*B*;are empty sets. - True or false. (
*A*;∪ ;*A*)^{c};= ; ∅ ;.^{c} - True or false. [
*A*;∩ (*B*;∪ ;*C*)]= (^{c}*A*;∩ ;*B*)^{c};*∩*;(*A ; ∩ ;C*)^{c} - True or false. ;
*n*(*A*) + ;*n*(*B*) = ;*n*(*A*; ∪ ;*B*) +*n*(*A ; ∩ ;B*) - True or false. If ;
*A ;∈ ;B*, then ;*n*(*B*) =*n*(*A*) + ;*n*(*A*^{c}*∩ ;*B). - True or false. The number of permutations of ;
*n*;distinct objects taken all together is ;*n*! - True or false. ;
*P*(*n*, ;*r*) = ;*r*! ;*C*(*n*, ;*r*).

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