Discrete Mathematics Answers

Develop truth tables and its corresponding Boolean equation for the following
scenarios.
a- The main function of automatic water level controller is to keep the water in
the tank between two levels : low level indicated by sensor A and high level
indicated by sensor B. It will automatically start the pump set as soon as the
water level falls below the sensor A (when A is low ), and shall switch off the
pump set when sensor B is high.
b- '' If the start button is ON and one of the two switches, door switch and
window switch, is ON, then the alarm system should turn ON.''

A number of science students prepared for examination in physics, chemistry and mathematics. Out of the number 15 took physics,23 took Maths and 20 took chemistry. 6 took physics and maths, 9 took maths and chemistry. all those who took physics also took chemistry. One of the students felt ill and fail to write the exams. How many students toa number of science students prepared for examination in physics, chemistry and mathematics. Out of the number 15 took physics,23 took Maths and 20 took chemistry. 6 took physics and maths, 9 took maths and chemistry. all those who took physics also took chemistry. One of the students felt ill and fail to write the exams. A. How many students took exactly one of the subjects? B. how many students took exactly two of the subjects? C. How many students prepare for the examination?

Does deductive reasoning always work? Elaborate your answer

Let A,B,C be subsets of a set. Prove that,
A ∩ B ⊆ C iff A ⊆ Bcompliment ∪ C.

In a road worthiness test on 40 cars. 60% passed. The number that failed had faults in clutch, brakes and steering as follows: Clutch only - 28; clutch and steering - 14; clutch, steering and brakes - 8; clutch and brakes - 20; brakes are steering only - 6.
The number of cars with faults in steering only is twice the number of cars with faults in brakes only.
(i) draw a Venn diagram to illustrate the information
(ii) how many cars had:
(a) Faulty breaks?
(b) Only one fault?

1. In a certain examination, 72 candidates offered Maths, 64 offered English, 62 offered French, 18 offered both Maths and English, 24 offered Maths and French, and 20 offered English and French. While 8 candidates offered all the three subjects. How many candidates were there for the examination?

Find in set builder notation the set of all positive integers a such that
a≡137 (mod 5).

A car number plate consists of a letter, followed by five numbers, and ended with three letters. How many car number plates can be formed? if required there must not be the same letter and no equal lift, and how many car number plates can be formed ?

The fibonacci sequence is defined as x0 = 0, x1 = 1 and xn+2 = xn +xn+1 , for all non negative integers n prove that, xm = xr+1xm-r + xrxm-r for all integers m ≥ 1 and 0 ≤ r ≤ m-1 and xd divides xkd for all integers k and d