Search & Filtering
Let A = {x € N: 3 ≤ x ≤ 13}, B = {x € N : x is even}, and C = {x EN: x is odd}.
(a) Find An B.
(b) Find A UB.
(c) Find Bn C..
(d) Find BUC.
Write the statements in symbolic form
, and
and the indicated letters to
represent compound statements.
a) Let s = “stocks are increasing” and i = ”interest rates are steady”.
i. Stocks are increasing but interest rates are steady.
ii. Neither are stocks increasing nor are interest rates steady
A group of students study at least one of the following subjects:biology, chemistry and physics. 36 of them study chemistry, 39 study biology and 41 study physics.15 study physics. 9 study all the three subjects. @draw a Venn diagram to illustrate this information.(b)from your diagram find:(1) the total number of students in the group.(2)the number of students who study only one subject.@the universal set U={2,3,5,7},p={2,5}and Q={5,7}find:(1)(PnQ),(2)P'UQ'. State the relationship between (1)and(2)(b)in a class of 50 students, 30 offer economics,17 offer government and 7 offer neither economics nor government. How many students offer both subjects.
Let A = {a,b,c,d}, B = {1,2,3}, and R = {(a,2), (b, 1), (c, 2), (d, 1)}.
(a)Is R a function?
(b)Is R−1 a function?
Explain your answers.
Prove or disprove the validity of the argument"every living things is a plant or an animal",Kamal's dog is alive and it is not a plant",All animals have heart",Hence "Kamal's dog has a heart".
a) Consider the full adder function: i-1 i i i i sum(c , x , y ) = (c , s) Where xi i i-1 , y are the i bits of the binary numbers X and Y, c is the carry in and the outputs are: th ci i , the carry out and s is the sum output. Write the equations o i i f both c and s in conjunctive normal form (CNF), i.e. in standard product of sums (SPOS).
b) As a result of a) above, design the corresponding circuit for the full adder, using only the NOR gates..
a) Consider the whole of the English words set. Suppose an English word x is related to another English word y if x and y begin with the same letter. i) Show that this is an equivalence relation. ii) Compute C(quadratic) and C(rhombus) iii) How many equivalence classes are there in all, and why? iv) What is the partition of the English words under this relation?
b) Consider Z, the set of integers. Suppose we define the relation: x is related to y if x - y > 3, x, y 0 Z. Determine whether or not the relation is i) reflexive ii) symmetric
a) Consider the following functional relation, f, defined as:
f : R \rightarrow R, f(x) = x2
Determine whether or not f is a bijection. If it is, prove it. If it is not, show why it is not.
b) Consider the set
F = {y | y = ax3 + b},
a, b being constants such that a \ne 0 and x \in R.
Is F equivalent to R? If so, prove it. If not, explain in details why it is not the case.a) Consider the whole of the English words set. Suppose an English word x is related to another
English word y if x and y begin with the same letter.
i) Show that this is an equivalence relation.
ii) Compute C(quadratic) and C(rhombus)
iii) How many equivalence classes are there in all, and why?
iv) What is the partition of the English words under this relation?
b) Consider Z, the set of integers. Suppose we define the relation: x is related to y if x - y > 3, x, y \in Z. Determine whether or not the relation isi) reflexive
ii) symmetric
iii) transitive
question 2
Consider the truth function
f(P, Q, R) = (P \rightarrow Q) \rightarrow Ra) Find a restricted statement form in conjunctive normal form (CNF) logically equivalent to f.
b) Find a restricted statement form in disjunctive normal form (DNF) logically equivalent to f.
#333702 on Dec 2022