###### GATE 2004-IT

October 5, 2023###### GATE 2004-IT

October 5, 2023# GATE 2004-IT

Question 4 |

Let R_{1} be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R_{2} be another relation from B to C = {1, 2, 3, 4} as defined below:

1. An element x in A is related to an element y in B (under R_{1}) if x + y is divisible by 3.

2. An element x in B is related to an element y in C (under R_{2}) if x + y is even but not divisible by 3.

Which is the composite relation R_{1}R_{2} from A to C?

R _{1}R_{2} = {(1, 2), (1, 4), (3, 3), (5, 4), (7, 3)} | |

R _{1}R_{2} = {(1, 2), (1, 3), (3, 2), (5, 2), (7, 3)} | |

R _{1}R_{2} = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)} | |

R _{1}R_{2} = {(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)} |

Question 4 Explanation:

From the given information,

R

where x+y is divisible by 3

R

where x+y is not divisible by 3

Then the composition of R

(x,z) ∈ R

Thus, R

R

_{1}={(1,2), (1,8), (3,6), (5,4), (7,2), (7,8)}where x+y is divisible by 3

R

_{2}= {(2,2), (4,4), (6,2), (6,4), (8,2)}where x+y is not divisible by 3

Then the composition of R

_{1}with R_{2}denotes R_{1}R_{2}, is the relation from A to C defined by property such as:(x,z) ∈ R

_{1}R_{2}, iff if there is a y ∈ B such that (x,y) ∈ R_{1}and (y,z) ∈ R_{2}.Thus, R

_{1}R_{2}= {(1,2), (3,2), (3,4), (5,4), (7,2)}Correct Answer: C

Question 4 Explanation:

From the given information,

R

where x+y is divisible by 3

R

where x+y is not divisible by 3

Then the composition of R

(x,z) ∈ R

Thus, R

R

_{1}={(1,2), (1,8), (3,6), (5,4), (7,2), (7,8)}where x+y is divisible by 3

R

_{2}= {(2,2), (4,4), (6,2), (6,4), (8,2)}where x+y is not divisible by 3

Then the composition of R

_{1}with R_{2}denotes R_{1}R_{2}, is the relation from A to C defined by property such as:(x,z) ∈ R

_{1}R_{2}, iff if there is a y ∈ B such that (x,y) ∈ R_{1}and (y,z) ∈ R_{2}.Thus, R

_{1}R_{2}= {(1,2), (3,2), (3,4), (5,4), (7,2)} Subscribe

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