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Mathematical Reasoning

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Statements and Logical Connectives

Subtopic

Statements and Logical Connectives under Mathematical Reasoning for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Consider pp: 'It is cold' and qq: 'It is snowing'. The symbolic form for 'It is not cold and it is snowing' is:

    A.

    ∼p∨q\sim p \vee q

    B.

    ∼p∧q\sim p \wedge q

    C.

    p∧∼qp \wedge \sim q

    D.

    ∼(p∧q)\sim (p \wedge q)

  2. 2.

    The negation of 'xx is not an integer' is:

    A.

    xx is a fraction

    B.

    xx is an integer

    C.

    xx is a natural number

    D.

    None of these

  3. 3.

    What is the truth value of (T∨F)∧T(T \vee F) \wedge T?

    A.

    True

    B.

    False

    C.

    Neither

    D.

    None of these

Download the worksheet for Mathematical Reasoning - Statements and Logical Connectives to practice offline. It includes additional chapter-level practice questions.

Implications, Converse, and Contrapositive

Subtopic

Implications, Converse, and Contrapositive under Mathematical Reasoning for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The contrapositive of the statement 'If pp, then qq' is equivalent to:

    A.

    The converse

    B.

    The inverse

    C.

    The original implication

    D.

    The negation

  2. 2.

    Converse of 'If x=yx = y, then x+z=y+zx + z = y + z' is:

    A.

    If x+z=y+zx + z = y + z, then x=yx = y

    B.

    If x≠yx \neq y, then x+z≠y+zx + z \neq y + z

    C.

    If x+z≠y+zx + z \neq y + z, then x≠yx \neq y

    D.

    If x=yx = y, then x+z≠y+zx + z \neq y + z

  3. 3.

    What is the inverse of: 'If a number is positive, then its square is positive'?

    A.

    If the square is positive, the number is positive

    B.

    If the square is not positive, the number is not positive

    C.

    If a number is not positive, its square is not positive

    D.

    If the number is positive, its square is not positive

Download the worksheet for Mathematical Reasoning - Implications, Converse, and Contrapositive to practice offline. It includes additional chapter-level practice questions.

Validating Statements

Subtopic

Validating Statements under Mathematical Reasoning for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    In mathematical logic, the statement "There exists a real number xx such that x2=xx^2 = x" uses which type of quantifier?

    A.

    Universal Quantifier

    B.

    Bi-conditional Quantifier

    C.

    Negation Quantifier

    D.

    Existential Quantifier

  2. 2.

    Consider the compound statement: "1010 is a multiple of 55 and 1010 is a multiple of 33". What is the truth value of this statement?

    A.

    True

    B.

    False

    C.

    Both True and False

    D.

    Cannot be determined

  3. 3.

    What is the negation of the statement: "All natural numbers are integers"?

    A.

    No natural numbers are integers.

    B.

    There exists a natural number which is not an integer.

    C.

    All integers are natural numbers.

    D.

    Some integers are not natural numbers.

Download the worksheet for Mathematical Reasoning - Validating Statements to practice offline. It includes additional chapter-level practice questions.