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Commutative law

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Write the component statements of the following compound statements and check whether the compound statement is true or false · (i) Venus is the smallest and. Jupiter is the largest planet of solar system. (ii) India is a country and Asia is a continent. (iii) Commutative law holds for addition and subtraction of rauonal number. (iv) Additive inverse exists for natural number and rational nutnber (v) 32 is a multiple of 2, 3 and 4.

Show that the operation * on Z define by a* b =a+b+1 for all a,b in Z Satisfies (i) the closure property (ii) the associative law and (iii) the commutative law ltrbgt (iv) find the identity element in Z (v) what is the inverse iof an element a in Z ?

Knowledge Check

  • Assertion: Vector addition is commutative. Reason: (vecA+vecB)!=(vecB+vecA)

    A
    If both assetion and reason are true and the reason is the correct explanation of the assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of the assertion
    C
    If assertion is true but reason is false
    D
    If the assertion and reason both are false.

  • If the matrix {:[(a,b),(c,d)]:} is commutative with matrix {:[(1,1),(0,1)]:} , then

    A
    `a=0,b=c`
    B
    `b=0,c=d`
    C
    `c=0,d=a`
    D
    `d=0,a=b`

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