Discrete Mathematics Answers

How many distinguishable permutations with repeated elements are there for the number 20366650?

MODULE 6:

Draw the logic diagram of the function and find for the

simplified Boolean expression of the following:

1. F(a, b, c) = ∑(0, 2, 3, 4, 5, 6)

2. F(a, b, c, d) = ∑(0, 2, 3, 4, 6, 8, 10, 12, 13, 14, 15)

3. F(a, b, c, d) = ∏(1, 2, 4, 5, 6, 7, 10, 11, 13, 15) 

1. Let p, q, r and s represent the following: Determine the truth value of each statement.

P: 2  is the smallest prime number.  True

q: The capital city of Camiguin is Mambajao.  True

r:  The sum of 2 odd numbers is odd. False

s: The diagonals of a parallelogram are congruent. False

Let p, q, r and s represent the following: Determine the truth value of each statement.P: 2 is the smallest prime number. Trueq: The capital city of Camiguin is Mambajao. Truer: The sum of 2 odd numbers is odd. Falses: The diagonals of a parallelogram are congruent. False

How many strings of length 5 can be made using the letters " ABCDE" which start with A and in which CD always comes together?

1 * 3!*2!

The police have three suspects for the murder of Janab Chaudary AllahDitta (Ch AD): Mr Chaloosak,Mr Maloosak and Mr Kabacha.

Chaloosak, Maloosak and Kabacha each declare that they did not kill Ch AD.

Chaloosak also states that Ch AD was a friend of Maloosak and that Kabacha disliked him.

Maloosak also states that he did not know Ch AD and that he was out of town the day Ch AD was killed.

Kabacha also states that he saw both Chaloosak and Maloosak with Ch AD the day of the killing and

that either Chaloosak or Maloosak must have killed him.

Can you determine who the murderer was if we know that:

a)one of the three men was guilty, the two innocent men are telling the truth, but the statement of guilty man may or may not be true?

b)innocent men do not lie?

Hint:

Translate the statements into logical expressions and reasoning from these expressions using

the truth tables.

Write CONTRPOSITIVE of the following statements.

a)If P is a square, then P is a rectangle.

b)If n is prime, then n is odd or n is 2.

c)If Aangloo is Meena's father, then Baangloo is her uncle and Bingli is her Aunt.

d)A positive integer is prime only if it has no divisors other than 1 and itself.

e)Being divisible by 3 is a necessary condition for this number to be divisible by 9.

Draw the logic diagram of the function and find for the

simplified Boolean expression of the following:

1. F(a, b, c) = ∑(0, 2, 3, 4, 5, 6)

2. F(a, b, c, d) = ∑(0, 2, 3, 4, 6, 8, 10, 12, 13, 14, 15)

3. F(a, b, c, d) = ∏(1, 2, 4, 5, 6, 7, 10, 11, 13, 15)

Write CONVERSE of the following statements.

a)If P is a square, then P is a rectangle.

b)If n is prime, then n is odd or n is 2.

c)If Aangloo is Meena's father, then Baangloo is her uncle and Bingli is her Aunt.

d)A positive integer is prime only if it has no divisors other than 1 and itself.

e)Being divisible by 3 is a necessary condition for this number to be divisible by 9.

Write NEGATION of the following statements (Careful, NEGATION is not the same as INVERSE)

a)If P is a square, then P is a rectangle.

b)If n is prime, then n i odd or n is 2.

c)If Aangloo is Meena's father, then Baangloo is her uncle and Bingli is her Aunt.

d)A positive integer is prime only if it has no divisors other than 1 and itself.

e)Being divisible by 3 is a necessary condition for this number to be divisible by 9.