Let A, B, C and D be four non-empty sets.

Question

Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A $$ \subseteq $$ B and B $$ \subseteq $$ D,
then A $$ \subseteq $$ C" is :

Accepted Answer

Contrapositive of p $$ \to $$ q is ~q $$ \to $$ ~p

If A $$ \subseteq $$ B and B $$ \subseteq $$ D,
then A $$ \subseteq $$ C means

(A $$ \subseteq $$ B) $$ \wedge $$ (B $$ \subseteq $$ D) $$ \to $$ (A $$ \subseteq $$ C)

Contrapositive is

$$ \sim (A \[ \subseteq $$ C) $$ \to $$ $$ \sim (A \[ \subseteq $$ B) $$ \vee $$ $$ \sim (B \[ \subseteq $$ D)

$$ \Rightarrow $$ A \nsubseteq  C $$ \to $$ (A \nsubseteq  B) $$ \vee $$ (B \nsubseteq  D)

Solutions · 1