Condider the following two statement

$( \exists x \in R)\ (\forall y\in s)\ (y < x)\\ ( \exists x \in R) (\forall y\in s)\ ( y > x) \\ (\exists r\in R)\ (\forall y\in s)\ (|y| < r)$

Determine which of these statements is true for each of the following choice of S

a (s) = [-3 , 10) (b) S = Q

Solution:

Here

$( \exists x \in R) (\forall y\in s) (y < x)\\ ( \exists x \in R) (\forall y\in s) ( y > x) \\ (\exists r\in R) (\forall y\in s)(|y| < r)$

a. All True b. All false

Write converse inverse and contrapositive of the statement. “ if x < 0 then $$x^2 – x > 0$$ “, Also write the negation of each statement.

Solution:

Given statement is

$' if\ x < 0\ then\ x^2 – x > 0 '$

Converse:

$if\ x^2 – x > 0\ then\ x < 0.$

Nagation:

$x^2 – x > 0\ and\ x > 0$

Inverse

$if\ x > 0\ then\ , x^2 – x < 0.$

Negation:

$x > 0\ and\ x^2 – x > 0$

Contrapositive:

$if\ x^2 – x < 0\ then\ x > 0$

Negation:

$x^2 – x < 0\ and\ x < 0$

Tags:

Categories:

Updated: