Tag: maths

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Multiple choice validating statements proofs in mathematics mathematical reasoning maths

"If it is a good watch then it is a Titan watch. It is a Titan watch, therefore, it is a good watch". This argument is _____________.

  1. valid

  2. invalid

  3. may be valid or invalid

  4. invalid if conditional connective is replaced by biconditional connective
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The argument exhibits the logical fallacy of affirming the consequent. The premise states if P then Q, and the second premise affirms Q, but this does not logically guarantee P.

Multiple choice validating statements proofs in mathematics mathematical reasoning maths

While simplifying $\sqrt { \frac { 1-cosx }{ 1+cosx }  } $, two students got the following two answers A & B.
A)  cosec x - cot x  (B)   $\frac { 1 }{ cosecx+cotx } $ What can you say about answers ?

  1. Both A & B are worng

  2. Both A & B are right

  3. A is right B is wrong

  4. B is right A is wrong
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice validating statements proofs in mathematics mathematical reasoning maths
State whether the statement
P: "if x is a real number such that $x^3+2x=0$, then $x$ is $0$"  is true/false

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation x^3 + 2x = 0 factors to x(x^2 + 2) = 0. Since x^2 + 2 is always positive for real numbers, the only real solution is x = 0.

Multiple choice validating statements proofs in mathematics mathematical reasoning maths

State whether the statement
P: "if x is a real number such that $x^3+2x=0$, then $x$ is $0$" is true/false.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation x^3 + 2x = 0 factors to x(x^2 + 2) = 0. Since x^2 + 2 is always positive for real numbers, the only real solution is x = 0.

Multiple choice validating statements proofs in mathematics mathematical reasoning maths

Choose the incorrect statements

  1. Digit at the units place of $3^{51}$ is $9$
  2. If $i-f=(9-\sqrt{82})^{11}$ and $< f < 1 $, then $'i'$ is an even integers
  3. If $7^{80}$ is divided by $13$, then the remainder is $9$
  4. If only $6^{th}$ term in the expression of $\left(\dfrac{x}{5}+\dfrac{2}{5}\right)^{n} $ ahs numerically greatest coefficient, then $n=7$
Reveal answer Fill a bubble to check yourself
A Correct answer