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C.   State whether the following statement is True or False.

                   1.   Scalar quantities consist both the magnitude as well as direction.
                   2.   A matrix comprising a single row is known as the row matrix.
                   3.   Mean is the average of all the elements in a dataset.

                   4.   Intersection allows the combination of two or more tables based on common attributes.
                   5.   A database is a collection of tables with related data.
                   6.   Frequency bins refer to the intervals between samples in the frequency domain.
                   7.   A sample rate of 100 Hz and an FFT size of 100 will result in 100 frequency intervals for a 100 Hz range.


                                                SECTION B (Subjective Type Questions)
              A.   Short answer type questions.
                   1.   Write the set for B = {x: x is a natural number less than 8}.

                   Ans.  B = {1,2,3,4,5,6,7}.

                   2.   Let U = {2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}.
                       Find A′, B′, A′ ∩ B′ and A ∪ B.

                   Ans.  U = {2, 3, 4, 5, 6},

                       A = {2, 3} and             B = {3, 4, 5}
                       A′ = {4, 5, 6}             B′ = {2, 6}
                       Hence, A′ ∩ B′ = {6}       Also, A ∪ B = {2, 3, 4, 5}.

                   3.   Identify and briefly explain the following relational operators:
                       i.  σ     ii. π      iii. ∩     iv. ∪

                   Ans.  •     Selection: This is a unary operation that selects only some of the tuples (records) of the relation. The selection
                           operation yields a subset of the tuples (records) from a relation (table) that satisfies a given condition.

                       •    Projection:  The projection of a relation is defined as a projection of all its tuples over some set of attributes.
                           This operation yields a vertical subset of the relation (table).
                       •    Intersection: The intersection operation is a binary operation. The intersection operation yields the common
                           tuples from the two tables.
                       •    Union: The union operation  combines  two or more relations (tables).  The resultant relation of the union
                           operation contains tuples that are in either of the relation or in both relations.

                   4.   Consider the following matrix A:





                       a.   Find the order of the matrix.

                       b.   Write the elements of a , a , a , a , a 23.
                                               13
                                                         24
                                                      33
                                                   22
                   Ans.  a.  Order of the matrix is 3×4.
                       b.  19, –2, –5, 12,  5  .
                                       2



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