Phyton

PS MATHS - SSLC - FIVE MARKS QUESTIONS AND ANSWERS
SSLC - MATHEMATICS (A  B) = {1, 2, 3, 4, 5, 6, 7} {2, 3, 5, 7}
FIVE MARKS QUESTIONS AND ANSWERS
= {(1, 2), (1, 3), (1, 5), (1, 7), (2, 2),
01. Let A = The set of all natural numbers less than 8, (2, 3), (2, 5), (2, 7), (3, 2), (3, 3),
B = The set of all prime numbers less than 8, C = The set (3, 5), (3, 7), (4, 2), (4, 3), (4, 5),
of even prime number. (4, 7), (5, 2), (5, 3), (5, 5), (5, 7),
Verify that(A B)  C = (A  C)(B  C) (6, 2), (6, 3), (6, 5), (6, 7), (7, 2),
A = {1, 2, 3, 4, 5, 6, 7} (7, 3), (7, 5), (7, 7)}
B = {2, 3, 5, 7}
A  C = {1, 2, 3, 4, 5, 6, 7} { 2 }
C={2}
= {(1, 2), (2, 2), (3, 2), (4, 2), (5, 2),
(A B)  C = (A  C)(B  C)
(6, 2), (7, 2)}
(AB) = {1, 2, 3, 4, 5, 6, 7} {2, 3, 5, 7}
(A  B)(A  C) = (1, 3), (1, 5), (1, 7), (2, 3), (2, 5),
= {2, 3, 5, 7}
(2, 7), (3, 3), (3, 5), (3, 7), (4, 3),
(A B)  C = {2, 3, 5, 7} { 2 }
(4, 5), (4, 7), (5, 3), (5, 5), (5, 7),
= {(2, 2), (3, 2), (5, 2), (7, 2)} ......
A  C = {1, 2, 3, 4, 5, 6, 7} { 2 } (6, 3), (6, 5), (6, 7), (7, 3), (7, 5),
= {(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (7, 7)} ......
(6, 2), (7, 2)} =  Hence Proved.
B  C = {{2, 3, 5, 7} { 2 } 03. Let A = { xW / x < 2}, B = { xN / 1 < x  4},
= {(2, 2), (3, 2), (5, 2), (7, 2)} and C = {3, 5}.
(A  C)(B  C) Verify that A  (BC) = (A  B)(A  C)
= {(2, 2), (3, 2), (5, 2), (7, 2)} ...... A = {0, 1}
= Hence Proved.
B = {2, 3, 4}
02. Let A = The set of all natural numbers less than 8,
C = { 3, 5 }
B = The set of all prime numbers less than 8, C = The set
A  (B C) = (A  B)(A  C)
of even prime number.
(B C) = {2, 3, 4}{ 3, 5 }
Verify thatA  (BC) = (A  B)(A  C)
A = {1, 2, 3, 4, 5, 6, 7} = {2, 3, 4, 5}
B = {2, 3, 5, 7} A  (B C) = {0, 1} {2, 3, 4, 5}
C={2} = {(0, 2), (0, 3), (0, 4), (0, 5),
A  (BC) = (A  B)(A  C) (1, 2), (1, 3), (1, 4), (1, 5)} ... 
(BC) = {2, 3, 5, 7} - { 2 } (A  B) = {0, 1} {2, 3, 4}
= { 3, 5, 7} {(0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4)}
A  (BC) = {1, 2, 3, 4, 5, 6, 7}  { 3, 5, 7}
(A  C) = {0, 1} { 3, 5 }
= {(1, 3), (1, 5), (1, 7), (2, 3), (2, 5),
= {(0, 3), (0, 5), (1, 3), (1, 5)}
(2, 7), (3, 3), (3, 5), (3, 7), (4, 3),
(A  B)(A  C) = {(0, 2), (0, 3), (0, 4), (0, 5),
(4, 5), (4, 7), (5, 3), (5, 5), (5, 7),
(6, 3), (6, 5), (6, 7), (7, 3), (7, 5), (1, 2), (1, 3), (1, 4), (1, 5)} ... 
(7, 7)} ...... =  Hence Proved.
PV THEVAR GOVT. HR. SEC. SCHOOL, KARUPPAMPULAM, NAGAI DT.

, PS MATHS - SSLC - FIVE MARKS QUESTIONS AND ANSWERS
04. Let A = { xW / x < 2}, B = { xN / 1 < x  4}, 06. If A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}, Show that
and C = {3, 5}. (A  A) = (B  B) (C  C).
Verify that A  (BC) = (A  B)(A  C) A = {5, 6},
A = {0, 1} B = {4, 5, 6},
B = {2, 3, 4} C = {5, 6, 7}
C = {3, 5} (A  A) = (B  B) (C  C)
A  (B C) = (A  B)(A  C) A  A = {5, 6}{5, 6}
(B C) = {2, 3, 4}{3, 5}= { 3 } = {(5, 5), (5, 6), (6, 5), (6, 6)} . . . . 
A  (B C) = {0, 1} { 3 }= {(0, 3), (1, 3)} ...  B  B = {4, 5, 6} {4, 5, 6}
(A  B) = {0, 1} {2, 3, 4} ={(4, 4), (4, 5), (4, 6), (5, 4), (5, 5),
= {(0, 2), (0, 3), (0, 4), (1, 2), (5, 6), (6, 4), (6, 5), (6, 6)}
(1, 3), (1, 4)} C  C = {5, 6, 7} {5, 6, 7}
(A  C) = {0, 1} {3, 5} = {(5, 5), (5, 6), (5, 7), (6, 5), (6, 6),
= {(0, 3), (0, 5), (1, 3), (1, 5)} (6, 7), (7, 5), (7, 6), (7, 7)}
(A  B)(A  C) = { (0, 3), (1, 3)} ...  (B  B) (C  C) = {(5, 5), (5, 6), (6, 5), (6, 6)} .... 
= Hence Proved. = Hence Proved.

05. Let A = { xW / x < 2}, B = { xN / 1 < x  4}, 07. Given A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4}, and
and C = {3, 5}. D={1, 3, 5},
Verify that (A  B)  C = (A  C)(B  C) check if (A  C)  (B  D) = (A  B) (C  D) is true?
A = {0, 1} A = {1, 2, 3},
B = {2, 3, 4} B = {2, 3, 5},
C = { 3, 5 } C = {3, 4},
(A  B)  C = (A  C)(B  C) D = {1, 3, 5}
A B = {0, 1}{2, 3, 4}= {0, 1, 2, 3, 4} (A  C)  (B  D) = (A  B) (C  D)
(A  B)  C = {0, 1, 2, 3, 4} { 3, 5 } A  C = {1, 2, 3}{3, 4} = { 3 }
= {(0, 3), (0, 5), (1, 3), (1, 5), B  D = {2, 3, 5}{1, 3, 5} = {3, 5}
(2, 3), (2, 5), (3, 3), (3, 5), (A  C)  (B  D) = { 3 } {3, 5}
(4, 3), (4, 5)} .....  = {(3, 3), (3, 5)} . . . . . . . 
(A  C) = {0, 1} { 3, 5 } A  B = {1, 2, 3}{2, 3, 5}
= {(0, 3), (0, 5), (1, 3), (1, 5)} = {(1, 2), (1, 3), (1, 5), (2, 2), (2, 3),
(B  C) = {2, 3, 4}{ 3, 5 } (2, 5), (3, 2), (3, 3), (3, 5)}
= {(2, 3), (2, 5), (3, 3), (3, 5), (4, 3), (4, 5)} C  D = {3, 4}{1, 3, 5}
(A  C)(B  C) = {(0, 3), (0, 5), (1, 3), (1, 5), = {(3, 1), (3, 3), (3, 5), (4, 1),
(2, 3), (2, 5), (3, 3), (3, 5) (4, 3), (4, 5)}
(4, 3), (4, 5) } .....  (A  B) (C  D) = {(3, 3), (3, 5)} . . . . . . . 
 =  Hence Proved. = Hence Proved.
PV THEVAR GOVT. HR. SEC. SCHOOL, KARUPPAMPULAM, NAGAI DT.

, PS MATHS - SSLC - FIVE MARKS QUESTIONS AND ANSWERS

08. Let A = { xN / 1 < x  4}, B = { xW / 0 x <  2} 10. Let A = {3, 4, 7, 8} and B = {1, 7, 10}. Which of the
and C = {xN / x  3}. following sets are relations from A to B?
Then verify that A  (BC) = (A  B)(A  C) ( i ) R1= {(3, 7), (4, 7), (7, 10), (8, 1)}
A = {2, 3}
( ii ) R2= {(3, 1), (4, 12)}
B = {0, 1}
( iii ) R3= {(3, 7), (4, 10), (7, 7), (7, 8), (8, 11),
C = {1, 2}
(8, 7), (8, 10)}
A  (BC) = (A  B)(A  C)
BC = {0, 1}{1, 2} = {0, 1, 2} A = {3, 4, 7, 8},

A  (BC) = {2, 3} {0, 1, 2} B = {1, 7, 10}
= {(2, 0), (2, 1), (2, 2), (3, 0), A  B = {3, 4, 7, 8} {1, 7, 10}
(3, 1), (3, 2)} . . . . 
= {(3, 1), (3, 7), (3, 10), (4, 1), (4, 7),
A  B = {2, 3} {0, 1}
(4, 10), (7, 1), (7, 7), (7, 10), (8, 1),
= {(2, 0), (2, 1), (3, 0), (3, 1)}
A  C = {2, 3} {1, 2} (8, 7), (8, 10)}

= {(2, 1), (2, 2), (3, 1), (3, 2)} ( i ) R1 is a relation from A to B.
(A  B)(A  C) = {(2, 0), (2, 1), (2, 2), (3, 0), ( ii ) R2 is not a relation from A to B.
(3, 1), (3, 2)} ....
( iii ) R3 is not a relation from A to B.
 =  Hence Proved.
09. Let A = { xN / 1 < x  4}, B = { xW / 0 x <  2} 11. Let A = {1, 2, 3, 7} and B = {3, 0, -1, 7}, which of
and C = {xN / x  3}. the following are relation from A to B?
Then verify that A  (BC) = (A  B)(A  C). ( i ) R1= {(2, 1), (7, 1)},
A = {2, 3} ( ii ) R2= {(-1 1)}
B = {0, 1}
( iii ) R3= {(2, -1), (7, 7), (1, 3)}
C = {1, 2}
( iv ) R4= {(7, -1), (0, 3), (3, 3), (0, 7)}
A  (BC) = (A  B)(A  C)
A = {1, 2, 3, 7}
BC = {0, 1} {1, 2} = { 1 }
B = {3, 0, -1, 7}
A  (BC) = {2, 3} { 1 }
A  B = {1, 2, 3, 7}  {3, 0, -1, 7}
= {(2, 1), (3, 1)} ....
A  B = {2, 3} {0, 1} = {(1, 3), (1, 0), (1, -1), (1 7), (2, 3), (2, 0),

= {(2, 0), (2, 1), (3, 0), (3, 1)} (2, -1), (2, 7), (3, 3), (3, 0), (3, -1), (3, 7),
A  C = {2, 3} {1, 2} (7, 3), (7, 0), (7, -1), (7, 7)}
= {(2, 1), (2, 2), (3, 1), (3, 2)} ( i ) R1 is not a relation from A to B.
(A  B)(A  C) = {(2, 1), (3, 1)} .... ( ii ) R2 is not a relation from A to B.
 =  Hence Proved. ( iii ) R3 is a relation from A to B.
( iv ) R4 is not a relation from A to B.
PV THEVAR GOVT. HR. SEC. SCHOOL, KARUPPAMPULAM, NAGAI DT.

, PS MATHS - SSLC - FIVE MARKS QUESTIONS AND ANSWERS

12. A company has four categories of employees given 13. If X = {-5, 1, 3, 4} and Y = {a, b, c}, then which of
by Assistants (A), Clerks (C), Managers (M) and an the following relations are functions from X to Y?
Executive Officer (E). The company provide 10,000, ( i ) R1= {(-5, a), (1, a), (3, b)}
25,000, 50,000 and 1,00,000 as salaries to the ( ii ) R2= {(-5, b), (1, b), (3, a), (4, c)}

people who work in the categories A, C, M and E ( iii ) R3= {(-5, a), (1, a), (3, b), (4, c), (1, b)}

respectively. If A1, A2, A3, A4 and A5 were ( i ) R1= {(-5, a), (1, a), (3, b)}

Assistants; C1, C2, C3, C4 were Clerks; M1, M2, M3
were managers and E1, E2 were Executive officers and if
the relation R is defined by xRy, where x is the salary
given to person y, express the relation R through an
ordered pair and an arrow diagram.
ARROW DIAGRAM.
X Y R1 is not a function as 4 X does not have an image in Y.
( ii ) R2= {(-5, b), (1, b), (3, a), (4, c)}




25,000



R2 is a function as each element of X has an unique
image in Y.
( iii ) R3= {(-5, a), (1, a), (3, b), (4, c), (1, b)}


SET OF ORDERED PAIR
 R = {(10,000, A1), (10,000, A2), (10,000, A3),
(10,000, A4), (10,000, A5), (25,000, C1),
(25,000, C2), (25,000, C3), (25,000, C4),
(50,000, M 1), (50,000, M2), (50,000, M3),
(1,00,000, E1), (1,00,000, E2)} R3 is not a function as 1 X has two images a Y and
b Y


PV THEVAR GOVT. HR. SEC. SCHOOL, KARUPPAMPULAM, NAGAI DT.