Answer
$F(A-B)\neq F(A)-F(B)\\
counter\,example:\\
$
$X=\left \{ 5,6 \right \},Y=\left \{ 7 \right \}\\
A=X,B=\left \{ 6 \right \}\\
F:X\rightarrow Y ,\,\,\,F(5)=F(6)=7 \\
A-B=\left \{ 5 \right \}\\
F(A-B)=F(\left \{ 5 \right \})=\left \{ 7 \right \}\\
F(A)=F(\left \{ 5,6 \right \})=\left \{ 7 \right \}\\
F(B)=F(\left \{ 6 \right \})=\left \{ 7 \right \}\\
F(A)-F(B)=\varnothing \\
F(A-B)=\left \{ 7 \right \}\,but\,F(A)-F(B)=\varnothing \\
so\,F(A-B)\neq F(A)-F(B)
$
Work Step by Step
$X=\left \{ 5,6 \right \},Y=\left \{ 7 \right \}\\
A=X,B=\left \{ 6 \right \}\\
F:X\rightarrow Y ,\,\,\,F(5)=F(6)=7 \\
A-B=\left \{ 5 \right \}\\
F(A-B)=F(\left \{ 5 \right \})=\left \{ 7 \right \}\\
F(A)=F(\left \{ 5,6 \right \})=\left \{ 7 \right \}\\
F(B)=F(\left \{ 6 \right \})=\left \{ 7 \right \}\\
F(A)-F(B)=\varnothing \\
F(A-B)=\left \{ 7 \right \}\,but\,F(A)-F(B)=\varnothing \\
so\,F(A-B)\neq F(A)-F(B)
$
