Answer to Question #286039 in Discrete Mathematics for Reens

Question

which of the following statements are true? justify your answers i) the contrapositive of "not a ⇒ not b' is "a&b', where a and b are two statements. ii) any set can be represented by the listing method

Answer 1

i) According to the definition, contrapositive of $P\implies Q$ is $\neg Q \implies \neg P$. So, contrapositive of $\neg a \implies \neg b$ is $\neg(\neg b)\implies \neg(\neg a)$ , or $b \implies a$ , which is not equal to a&b. So, the first statement is false

ii) Listing method is a method of presenting the set when it's element are written in curly brackets and separated by comma. That means that only sets with finite amount of elements can be presented in such a way. So, this statement is also false