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draw the hasse diagram for the poset({1,3,6,9,12}) hence determine whether it is a lattice

 {x | x is a real number such that x2 = 1}


Oliveira, Anibal, Julia and Andres are planning to rob a bank. To hide their true identities, they came up with the idea of using the names of cities as aliases, namely, Manila, Tokyo, Rio and Berlin. Berlin is twice as old as Julia. Anibal and Manila used to be drug traffickers. Aliveira and Berlin are the seniors in the team. Tokyo is married while Anibal is single.Who is Berlin?
JuliaAnibalAndresOliveira

A magic square is an arrangement of n2 numbers into n rows and n columns using distinct numbers from 1 up to n2 such that the sum in any row, any column or any of the two diagonals is fixed. Consider the 4 by 4 magic square below:


a1 a5 2 13a2 10 11 a7a3 6 a4 124 15 a6 1
What is the value of a1 ?

What is the units digit in the expansion of 2 to the power of 727 ?


8

4

2

6

Use generating functions to solve the recurrence relation an = 7an−1 −

16an−2 + 12an−3 + n4n

, where a0 = −2, a1 = 0, a2 = 5.


Use rules of inference to show that the hypotheses “If the weather is not

too hot or not too cold, then the game will be held and a prize-giving

ceremony will occur,” “If the game is held then the VC will give a speech,”

“The VC did not give a speech,” imply the conclusion “The weather was

too hot.”


What is nested Quantifier? Is order important for nested quantifier?

Explain your answer with appropriate example.


The negation of the statement " 52 is divisible by 4 and 7" is


3. Proof that an undirected graph has an even number of vertices of odd degree.


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