Math Answers

Suppose that, in the circuit for a 2-bit comparator, we wanted to allow for inputs from the

higher byte comparisons, xH < yH, xH = yH, xH > yH, so that we could now use a 2-bit

comparator in cascades for building comparators for numbers with more than 2 bits.

a) Re-write the equations for a 2-bit comparator that would allow for the inputs: xH < yH,

xH = yH, xH > yH.

b) Re-draw the corresponding circuit diagram.

Question 2:

Consider the following narration:

If equality of opportunity is to be achieved then those people previously disadvantaged should be

given special opportunities. If those people previously disadvantaged should be given special

opportunities then some people should receive preferential treatment. If some people receive

preferential treatment then equality of opportunity is not to be achieved. Some people are not going

to receive preferential treatment. Therefore, equality of opportunity is not to be achieved.

a) Encode the argument in Propositional Calculus.

b) As a result of a) above, use logical rules of inference to show that the given argument is sound/valid.

HINT: For any statement forms, P and Q P \rightarrow Q = ¬Q \rightarrrow ¬P.

King Corporation Limited (KCL), a producer of electricity, is considering to expand its operation by adding 5 generators. The cost of these generators would be Tk. 100 million. The expected life of the generators is 5 years. The addition of these generators will result in cash inflows of Tk. 50 million per year for 5 years. Cash outflows would be 50% of cash inflows. KCL uses straight line method of depreciation and expects no salvage value from the generators at the end their service lives. IDLC, a leading Non-Bank Financial Institution, offered KCL to lease the generators for 5 years. The lease payments to be made at the beginning of each year would be Tk. 24 million. The annualized risk-free rate of return is 7%. Tax rate for both KCL and IDLC is 30%.

f. Assume now that KCL’s tax rate is 10% while IDLC’s tax rate remained at 30% and IDLC revises its offer to reduce the lease payments to Tk. 22 million a year.

The force of interest at any time t, (measured in years) is given by

δ(t) =



0.07 − 0.005t, 0 ≤ t < 5

0.06 − 0.003t, 5 ≤ t < 10

0.03, t ≥ 10

What is the total accumulated in value at any time t (> 0) of investments of $100 at times 0, 4 and 6?

Draw hasse diagram representing the positive divisor of 36 and show digraph to It?

Sketch the region enclosed by the curves and find its area.

y=e^x, y=e^8x, x=0, x=ln2

We consider the point M(1, 0, 2) and the lines d1 :    x = t + 1, y = −t + 2, z = t − 1 and d2 : x = y = z. (a) Find the director vectors of the lines d1 and d2. (b) Find the angle between the lines d1 and d2. (c) Write the equation of the plane passing through the point M that is perpendicular to the line d2

. Find a basis for the orthogonal complement of the vector v(1, 3,−2) of the euclidean vector space (R 3 , ·). Argue whether this basis is orthonormal or not.

Study whether the vectors v1(1, 1, 2), v2(2, 3, 0), v3(3, 4, 2) in R 3 are linearly dependent. If so, find the linear dependency relation

 Study whether the vectors v1(1, 1, 2), v2(2, 3, 0), v3(0, 1, 2) in R 3 are linearly independent.