Solved: Given three sets A, B, and C. Suppose we know that the union of the three sets has cardinality 182. Further, |A| = 92, |B| = 41, |C| = 118. Also, |A ∩ B| = 15, |A ∩ C| = 42, and |A ∩ B ∩ C| = 10. Find |B ∩ C|.

6. Use truth tables to determine whether the argument form is valid. [5 Marks] a. There is an undeclared variable or there is a syntax error in the ﬁrst ﬁve lines. b. If there is a syntax error in the ﬁrst ﬁve lines, then there is a m…

∀x∃y(x + y = 2 ∧ 2x − y =1

A palindrome number is a number that is read similarly backwards. How many possible 5-digit palindromic numbers are there? A. 608 B. 648 C. 688 D. 728

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Make negation of the following statements. I4) All students have taken a course in mathematics. 15) Some students are intelligent, but not hardworking

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Alice decides to set up an RSA public key encryption using the two primes p= 31 and p= 41 and the encryption key e= 11.You must show all calculations, including MOD-calculations using the division algorithm! Bob decides to send the me…

1. Discuss two real world binary problems in two different fields using applications of Boolean Algebra.

Write the following sets in the roster/tabular form: a. G = {x : x ∈ N, 5 < x < 12} b. H = {x : x is a multiple of 3 and x < 21} c. I = {x : x is perfect cube 27 < x < 216} d. J = {x : x = 5n - 3,n ∈ W, and n < 3}

prove with inductions that n^2+n divisible by 2

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In a survey, 2000 people were queried if they read India Today or Business Times. It was found 1200 read India Today, 900 read Business Times and 400 read both. How many read at least one magazine

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If p is true, q, r, and s are false, find the truth value of the proposition. ¬(¬𝑝 ∨ 𝑞) ∨ ¬((𝑝 ∧ ¬𝑟) → ¬𝑠)

There are 7 groups in a picnic who has brought their own lunch box, and then the 7 lunch box are exchanged within those groups. Determine the number of ways that they can exchange the lunch box such that none of them can get their own.

How many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of a particular suit are chosen

There are 7 groups in a picnic who have brought their own lunch box, and then the 7-lunch boxes are exchanged within those groups. Determine the number of ways that they can exchange the lunch box such that none of them can get their …

Draw the Hasse diagram for (i) Pi = {1, 2, 3, 4, 12} and < is a relation such that x < y if x divides y.

Let P = {1,2,3,4} and R = {(1,1), (2,1), (1,2), (2,2), (3,2), (3,4), (4,3), (4,4)} which is a relation on P. Represent this relation as a directed graph. Check whether this relation is an equivalence relation or not.

For discrete structures there are n exams to check and there are k graders. To guarantee a high quality of grading, every exam may be checked by any number of graders (but always at least by one grader). This means that summed all tog…

An orientation of a graph G = (V,E) is any directed graph G'= (V,E) arising by replacing each edge {u, v} belonging to E, by the directed edge (u, v) or by the directed edge (v, u). Show that for every planar graph there is an orienta…

Draw the De Bruijn graph for 2-tuples with digits 0,1,2, and 3. Make sure to add matching labels to all vertices and edges.

A group of 21 students participates in a discrete mathematics competition. There are Q questions that have to be answered. For each question exactly 4 students are assigned to work together, while the others take a short break. The qu…

Find the sum of product expansion of the Boolean function f(x,y,z) = (x+z)y

For discrete structures there are n exams to check and there are k graders. To guarantee a high quality of grading every exam may be checked by any number of graders (but always at least by one grader). This means that summed all toge…

Let ρ be a relation on a set A. Define ρ −1 = { | ∈ ρ}. Also for two relations ρ, σ on A, define the composite relation ρ ◦ σ as (a, c) ∈ ρ ◦ σ if and only if there exists b ∈ A such that ∈ ρ and ∈ σ. Prove the following assertions (a…

the number of combinations of five objects taken two at a time is?

Show that the propositions pi, p2, p3, and p4 can be shown to be equivalent by showing that p1 ↔ p4, P2 ↔ P3, and p1 ↔ p3.

Show that ~ (p → q) and p ∧~q are logically equivalent. (Hint: you can use a truth table to prove it or you apply De Morgan law to show the ~(p → q) is p ∧~q.

The Mathclub, VIT-AP wants to conduct a group event for its members. So the club president has to fix the group size the event. When he tries to fix the size to be 5 members in each group, 4 members are left; when he tries to fix the …

Make a truth table for the given expression. 12. (~p∧q) ∨ (p∧~q) 13. (p∧~q) ∨ r 14. ~[(p∧~q) ∨ ~p] 15. (p∨q) ∧ ~(~q∧r) 16. (~p∧q) ∨ (~p∨q) 17. ~[(p∨q) ∧ ~q]

Show that among 2000 student in a school, at least six were born on the same day of the leap year

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translate the statement "The product of any two positive integers is always positive"into logical expression(using Nested Quantifiers)

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He relation (a,b) such that "a" and "b" have the same age ,is defined on the sets of all people.Is it equivalent relation?

Indian Cricket team was doing catching practice .The fielding coach informed then that they will throw ball to 4 other players done this ,but others did not throw any ball to catch.how many players received the ball including first pl…

If we have two graph G = (V, E) and G0 = (V, E0 ) on the same set V of vertices we call the union G ∪ G0 the graph (V, E ∪ E0 ). Next we have two claim about the chromatic number χ(G ∪ G0 ) of G ∪ G0 .Prove that χ(G∪G0 ) ≤ χ(G)∗χ(G0 )…

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Are these system specifications consistent? ”The file system is not locked only if new messages will be queued. If the file system is not locked, then the system is functioning normally, and conversely. For new messages are not queued…

USING MATHEMATICAL INDUCTION P(n)=1+22+2n+........+2n= 2n+1 - 1

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how many three letter words can be formed by the word letter EQUATION

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Q(X,y):X+y >or=7 then what is truth value of∀x∃yQ(x,y)

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How many 3 letter words can be formed by the word letter EQUATION

Given three sets A, B, and C. Suppose we know that the union of the three sets has cardinality 182. Further, |A| = 92, |B| = 41, |C| = 118. Also, |A ∩ B| = 15, |A ∩ C| = 42, and |A ∩ B ∩ C| = 10. Find |B ∩ C|.

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