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Mathematical Reasoning Test - 24

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Mathematical Reasoning Test - 24
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  • Question 1
    1 / -0
    The metal that does not displace hydrogen from an acid is
    Solution

    In an electrochemical series, all metals above hydrogen in the acitivity series will displace hydrogen form an acid .

    Here, Ca, Al and Zn are placed  above hydrogen hence these metals can displace hydrogen , whereas , Hg placed below the hydrogen. So, it does not displace hydrogen from an acid.

  • Question 2
    1 / -0
    Consider the statement, Given that people who are in need of refuge and consolation are apt to do odd things, it is clear that people who are apt to do odd things are in need of refuge and consolation. This statement, of the form$$ (P \Rightarrow Q) \Rightarrow (Q \Rightarrow P)$$, is logically equivalent to
    Solution
    Given statement is "people who are in need of refuge and consolation are apt to do odd things"
    It is in the form of $$p\Rightarrow q$$ , where $$p$$ is "in need of refuge and consolation" and $$q$$ is "apt to do odd things"
    So $$q\Rightarrow p$$ is equivalent to "people who are apt to do odd things are in need of refuge and consolation"
    Therefore option $$C$$ is correct
  • Question 3
    1 / -0
    Negation of "$$2+3=5$$ and $$8<10$$" is
    Solution
    Let $$p:2+3=5$$
    and $$q=8<10$$
    Given proposition is $$p\wedge q$$
    Its negatition is $$\sim (p\wedge q)=\sim p\wedge \sim q$$
    $$\therefore$$ We have $$2+3\ne 5$$ or $$8\nless 10$$
  • Question 4
    1 / -0
    The inverse of the proposition $$(p\wedge \sim q)\Rightarrow r$$ is
    Solution
    Inverse of $$p\Rightarrow q$$ is $$\sim p\Rightarrow \sim q$$

    $$\therefore$$ Inverse of $$(p\wedge \sim q)\Rightarrow r$$ is

    $$\sim(p\wedge \sim q)\Rightarrow \sim r$$

    i.e, $$(\sim p\vee q)\Rightarrow \sim r$$
  • Question 5
    1 / -0
    Which of the following is the inverse of the proposition : 'If a number is a prime then it is odd"?
    Solution
    Let  $$p:$$ Number is prime
    and $$q:$$ Number is odd

    The given statement is $$p \rightarrow q$$

    Its inverse is $$\sim p \rightarrow \sim q$$

    Therefore, the inverse is "If a number is not a prime then it is not odd." 

    So, option B is correct.
  • Question 6
    1 / -0
    Which of the following is not proposition?
    Solution
    $$\textbf{Step 1: Finding the options which are not a proposition}$$
                     $$\text{Looking at option A, 3 is prime}$$
                     $$\text{This can be classified as true unanimously, therefore it is a proposition}$$
                     $$\text{Looking at option B, }\sqrt2\text{ is irrational}$$
                     $$\text{This can be classified as true unanimously, therefore it is a proposition}$$
                     $$\text{Looking at option C, Mathematics is interesting}$$
                     $$\text{This can be classified as true or false unanimously, therefore it is not proposition}$$
                     $$\text{Looking at option D, 5 is an even integer}$$
                     $$\text{This can be classified as false unanimously, therefore it is a proposition}$$
    $$\textbf{Hence  Option C is correct}$$
  • Question 7
    1 / -0
    Given: All seniors are mature students. Which statement expresses a conclusion that logically follows from the given statement?
    Solution
    Given that all seniors are mature students ($$p\Longrightarrow q$$)
    $$p\Longrightarrow q$$ is equivalent to $$\sim q\Longrightarrow \sim p$$
    So the correct answer is , If Bill is not a senior , then he is not a mature senior
    So the correct option is $$C$$
  • Question 8
    1 / -0
    The inverse of statement " If a quadrilateral is a rectangle,then it has two pairs of parallel sides."
    Solution
    The inverse of statement " if a quadrilateral is a rectangle, then it has two pairs of parallel sides" is
    " If a quadrilateral is not a rectangle then it does not have two pairs of parallel sides".
  • Question 9
    1 / -0
    STATEMENT: All cabbages are red.
    Which of the following statements shows that the statement above is FALSE?
    Solution
    Given statement is that All cabbages are red
    E. Option shows that the statement above is false because it says that Keisha is eating a green cabbage, which means that all cabbages are not red that's why Keisha is eating a green cabbage.
    Rest other statements does not falsify the statement that all cabbages are red.
  • Question 10
    1 / -0
    "If p, then q" is logically equivalent to which of the following?
    I. If q, then p
    II. If not p, then not q.
    III. If not q, then not p
    Solution
    "If $$p$$ , then $$q$$" means  $$ p \Rightarrow q$$
    The explanation for the given statement is if $$p$$ happens then $$q$$ will happen , which implies if $$q$$ wont happen then $$ p$$ also wont happen
    Therefore "If $$p$$, then $$q$$" implies "If not $$q$$ , then not $$p$$"
    Therefore the correct answer is option $$B$$
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