Question 1 (45 marks)a) For each of the following statements, write the converse, inverse and...

Question

Question 1 (45 marks)a) For each of the following statements, write the converse, inverse and contrapositivestatement. Use p = hypothesis and q = conclusion. Also, provide the mathematicalnotations for the respective statements.(i) If the weather is nice, then I will wash the truck (5 marks)(ii) If � >	5, then, �2	>	25	 (5	marks)(iii)~� →	(~�∆�)		 	 	 	 	 	 	 (5	marks)b) Write each of the following statements in the symbolic form and determine whichpairs (if any) are logically equivalent. Ensure that you explain the steps taken andthe reason for your decision.(i) If	the	goods	are	unsatisfactory,	then	your	money	will	be	refunded.(ii) Goods	satisfactory	or	money	refunded.(iii) If	your	money	is	not	refunded,	then	the	goods	are	satisfactory.(iv) If	the	goods	are	satisfactory,	then	your	money	will	not	be	refunded.(15 marks)c) Show that (p ∨ q) ∧ (r ∨ ¬ q) → (p ∨ r) is a tautology. Ensure that you explain thesteps taken and the reason for your decision. (15 marks)Question	1A	Marking	Scheme• Explanation	of	each	step	– 5	marks• Workings	– 10	marksQuestion	1B Marking	Scheme• Explanation	of	each	step	– 5	marks• Workings – 10 marks2Question 2 (30 marks)Use mathematical induction to prove the following formulae for every positive integer na XXXXXXXXXX4.5 + ⋯ +1�(� + 1)(� + 2) = �(� + 3)4(� + 1)(� + 2)Ensure that you explain the steps taken. (15 marks)b)1! + 3! + 5! + ⋯ + (2� − 1)! = �"(2�" − 1)Ensure that you explain the steps taken. (15 marks)Question	2A Marking	Scheme• Explanation	of	each	step	– 5	marks• Workings – 10 marksQuestion	2B Marking	Scheme• Explanation	of	each	step	– 5	marks• Workings – 10 marks

Rajeswari · Accepted Answer

75202 assignment
Qno.1
a) 
	 
	 
	 
	p = hypothesis
	q=conclusion
	Notation
	Nature
	i.
	Statement
	If the weather is nice, then I will wash the truck
	Weather is nice
	I will wash the truck
	p-->q
	Conditional
	 
	Converse
	If I wash the truck then the weather is nice
	 
	 
	q-->p
	Conditional
	 
	Inverse
	If the weather is not nice, then I will not wash the truck
	 
	 
	~p --> ~q
	Conditional
	 
	Contrapositive
	If I do not wash the truck, then weather is not nice.
	 
	 
	~q-->~p
	Conditional
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	ii. 
	Statement
	If n > 5, then, n^2 > 25
	n>5
	n^2>25
	p-->q
	 
	 
	Converse
	If n^2>25, then n>5
	 
	 
	q-->p
	Conditional
	 
	Inverse
	If n is not greater than 5, then  n^2 is not greater than 25.
	 
	 
	~p --> ~q
	Conditional
	 
	Contrapositive
	If n^2 is not greater than 25, n is not greater than 5
	 
	 
	~q-->~p
	Conditional
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	iii.

Question 1 (45 marks)a) For each of the following statements, write the converse, inverse and contrapositivestatement. Use p = hypothesis and q = conclusion. Also, provide the mathematicalnotations...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment