(4) (15 Points): Consider the following premises. 0 If Mr. Jones resigns the pre
ID: 3891059 • Letter: #
Question
(4) (15 Points): Consider the following premises. 0 If Mr. Jones resigns the presidency, then Mr. Williams becomes president p: Mr. Jones resigns the presidency o q: Mr. Williams becomes president o )If Mr. Williams is president, then prices will tise or productivity will fal. o qMr. Williams is president o r: the prices will rise s: productivity will fall (üi) Mr. Jones has resigned and productivity increased. o o p: Mr. Jones has resigned o s: Productivity increased Prove or disprove that prices will increase by translating these premises into logical notation and supplying a proper argument using the Rules of Inference and Laws of Logic.Explanation / Answer
Hi,
Given, Mr jones has resigned i.e P is True, alsp productivity increased i.e s is true too
drawing the truth table row for this ,
now since p->q, i.ei if p then q, so P is true implies q is true
p q s r
1 1 1
now r can be 0 or 1, lets consider both the cases, and see if all conditions hold,
in the second equation q->(r or s) where s is productivity will fall, but here productivity increases, hence s is 0
p q s r p->q r or s q-> (r or s) p and ~s(since in this condition, s is production increase)
1 1 0 0 1 0 0 0
here we can see, the conditions dont hold when r=0, lets check at r=1
p q s r p->q r or s q-> (r or s) p and ~s
1 1 0 1 1 1 1 1 //here we can see all condition are satisfied, hence r=1 is implied, i.e prices will increase
Thumbs up if this was helpful, otherwise let me know in comments
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