Discrete Mathematics ADP 2 Semester/Term UOS — University of Sargodha 2024

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ADP 2* Term Xs

subiccti LL Paper; Discr “MPC-1V

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ime Allowed: 02:30 Hours :

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We: Objective part is compulsory. Attempt an Be AR

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Objective Part ll

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Ll. Write short answers of the following in 2-3 li T——

1. Let A be the set of odd positive intege, than

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il. + Using truth table determine whether \( D = q)) = = Rology?

the LetA = fa, bye}, B= {x,y}, and C = B01). Find ©

iv. Determine whether /: Z x Z — Z is of ££ = Teak

v. « Show that p — (pV q) is a tautology ou isin

vi. Write any two rules of inference.

vii... What is greedy algorithm?

ix. What is arelation on a set?

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xi... What is a bipartite |

xii. + Define a tree. i

Subjective (3*12)

= Find a counter cxample if possible, to thes universally quantified statements,

for all variables consists of all integers?

a) IXVY(x2 =y: 2 x=y

b) vx3y 2d 1

¢) Vx¥y(xy = x al

~ Compute Uf; 4; and NZ A;such that 4;= wa 2 |

~ Solve the eggycnce Felation 2x. HY id, el, Ayla

~ Let fbe the function from {w, x, y, 2} t0 10g,2,7; WIEL/AW

Isfa bijection give raemons SRL J, tt finds the farthes

Given an array All..n] jr rans 3 Fo Sorin. [farthest baie lsat

determine tk or = > |

absolute difference is the largest]. |

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