Mathematical Logic - Mathematics - Assignment

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Question Text

Question 2 :
$3x + 2x = 5P$, what will come at place of P

Question 7 :
Check if the given statement is true or false.<div>$x(3x + 2) = 3x^2 + 2$</div>

Question 8 :
Here are some words translated from an artificial language $ mie \ pie \ is \ blue \ light$ $ mie \ tie \ is \ blue \ berry$ $ aie \ tie \ is \ rasp \ berry$ Which words could possibly mean "light fly"?

Question 9 :
Assertion: Two distinct lines cannot have more than one point in common. Reason: Any number of lines can be drawn through one point.

Question 10 :
State whether the following statement is True or False. The sum of two odd numbers and one even number is even.

Question 11 :
Which is logically equivalent to "If today is Sunday Matt cannot play hockey"?

Question 13 :
The contrapositive of : "If two triangles are congruent then they are similar" is

Question 14 :
The disjunction of the statements "Hyderabad is in India; $2+2=4$", is

Question 15 :
<div>State the following statement is True or False </div>The truth value of "$4$ is even and $8$ is odd" is True

Question 16 :
State whether the following statement is true or false. The sum of two even numbers is even.

Question 17 :
If quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.

Question 18 :
Find the counter example of the .statement "Every natural number is either prime or composite''.

Question 21 :
"If Deb and Sam go to the mall then it is snowing" Which statement below is logically equivalent?

Question 24 :
lf $P(n)$ be the statement $n(n+1),\;n \in N$ is even, then

Question 25 :
Mary says "The number I am thinking is divisible by 2 or it is divisible by 3". This statement is false if the number Mary is thinking of is

Question 26 :
State whether the following statement is True or False. The sum of three odd numbers is even.

Question 27 :
Select and write the correct answer from the given alternative of the following question: If $ p \wedge q $ is false and $ p \wedge q $ is true, then __________ is not true.

Question 28 :
Consider the following statements (1) $x - 2$ is a factor of $x^{3} - 3x^{2} + 4x - 4$ (2) $x + 1$ is a factor of $2x^{3} + 4x + 6$ (3) $x - 1$ is a factor of $x^{5} + x^{4} - x^{3} + x^{2} - x + 1$. Of these statement.

Question 29 :
State whether the following statements are true or false. Give reasons for your answers. For any real number $x, x^2 \geq 0$.

Question 33 :
$x + 2x + 3x = M$ find value of M

Question 34 :
State whether the following statement is True or False. $2$ is the only even prime number.

Question 35 :
Select and write the correct answer from the given alternative of the following question: If $ A = \left \{1 , 2 , 3 , 4 , 5 \right \} $ then which of the following is not true ?

Question 36 :
State whether the following statement is True or False. All even numbers are composite numbers.

Question 37 :
Consider the sentence: x<5 Which of the following integers makes this open sentence true?

Question 38 :
If p : A man is happy q : A man is rich Then, the statement, "If a man is not happy, then he is not rich" is written as

Question 40 :
$5y + 2y + 7y = M$ find value of $M$

Question 41 :
State True or False. <div>If two circles are equal, then their radii are equal. </div>

Question 42 :
If statement $p \rightarrow (q \vee r)$ is true then the truth values of statements p, q, r respectively

Question 43 :
The disjunction of the statements, "It is raining; The sun is shining" is

Question 44 :
Let $p, q$ and $r$ be any three logical statements. Which one of the following is true?

Question 46 :
State whether true or false.<div>The sum of the interior angles of a quadrilateral is $350^o$.</div>

Question 47 :
State whether the following statement is True or False. The product of three odd numbers is odd.

Question 48 :
Check whether the given statement is true or false.<div>$4(x- 5) = 4x- 5$</div>

Question 49 :
Which of the following statements is logically equivalent to "The solution is easy if you read the question carefully."?

Question 50 :
Earth is a planet. Choose the option that is a negation of this statement.

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