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a) Using Karnaugh map, show
X': A'BC'D'+ ABC'D'+ A'BCD'+ ABCD' (b) If R is an equivalence relation on set A, prove that R-1 is also an equivalence relation.
(c) Explain Konigsberg's 7 bridges problem and Euler's solution to it.
lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x? Ans) all no.s are positive or 0. so limit is either positive
Determine that in a Boolean algebra, for any a and b, (a Λ b) V (a Λ b' ) = a. Ans: This can be proved either by using the distributive property of join over meet (or of mee
project assignment of page no.19 question no.2
three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.
X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally. Given that XZY=90 o , w
pythagoras theorem
Example: Write down the equation of the line which passes through the two points (-2, 4) and (3, -5). Solution At first glance it might not appear which we'll be capable to
(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads. (b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},
Symmetry Definition : A line of symmetry divides a set of points into two halves, each being a reflection of the other. Each image point is also a point of the set. Defin
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is
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