Problem $6(5$ points$)$

Show that these statements are inconsistent, in other words, show the conjugation of these

statements is a contradiction using laws of the logic. Use as many rows as you need $($you

could combine the steps if they are using the same law$)$ but the expression must end with

False $($F $).$

$1.$ If Alex does not pass the exam, then he will not receive a scholarship. $($p $->$s$)$

$2.$ If Alex does not receive a scholarship, then he cannot afford to travel. $($s $->$t$)$

$3.$ If Alex participates in the workshop, then he can afford to travel. $($w $->$ t$)$

$4.$ Alex does not pass the exam but he participates in the workshop. $($p $$ w$).$