How to I prove the equivalence of $f(S_1 \cup S_2)$ and $f(S_1) \cup f(S_2)$ (Discrete Mathematics)
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
95935
Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
99662
proving than every $2\times 2$ is similar to a united form
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
89167
Cardinality of equivalence relations in $\mathbb{N}$
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
134120
Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
65977
Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$