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This is solution to assignment of Basic Mathematics course. This was submitted to Karunashankar Sidhu at Institute of Mathematical Sciences. It includes: Logic, connective, Truth, Table, Demorgan, Negotiation, Ordered, Pairs, Solution, Instructions, subset
Typology: Exercises
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Maximum Marks: 20 Due Date: April 18, 2012
DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
- To solve this assignment, you should have good command over 1 - 8 lectures. Try to get the concepts, consolidate your concepts and ideas from these **questions which you learn in the 1 to 8 lectures.
Question 1; Mark:3+7= (i) Determine which logical connective can be used here. (a) John is tall and thin. (b) Mathematics is not difficult. (c) The bus was late or I am in a hurry. Solution: (a) (b) ~ (c) (ii)
Construct a truth table of (p q) ~ (p q) Solution: p q (^) p q p q ~( p q) (p q) ~ (p q) T T T T F F T F F T F F F T F T F F F F F F T F
Question 2; Marks: 2+3= (i) Use De Morgan’s law to write the negation of 13 x 9 Solution: 13 x 9 means that -13 x and x< By De Morgan’s law, the negation is -13>x or x 9 (ii) Find x & y where (x+y,4x)=(3,8) Solution: Two ordered pairs are equal if and only if the corresponding components are equal. So x+y=3 and 4x= 4 x 8 x 8 / 4 2 2+y=3 y=1 so x=2 and y=
Question 3; Marks:3+2= (i) Determine whether each of the following statement is true or false. (1) {1} {1, 2,3} false because{1}is a subset of {1,2,3}not a member. (2) {1, 2,3} True because is a subset of every set. (3) {1, 2} {1, 2,3, 4} True because {1,2}is a subset of {1,2,3,4}.
(ii) Determine whether each of the following is a set or not. Justify your answer. A={10,20,30,40,50,60} B={1,2,3,4,1,5,6,7,5} Solution: A ={10,20,30,40,50,60} is a set. B={1,2,3,4,1,5,6,7,5} is not a set due to repetition of ‘1’ and ‘5’.