Recent questions in Discrete Mathematics

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Suppose A is a 12 by 9 incidence matrix from a connected (but unknown) graph with 12 edges and 9 nodes. Then how many columns of A are independent?what this question want...
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96
Is the simplification that I have encircled, done right? because according to negation law (r ∨ ¬ r) ≡ T.
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97
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98
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100
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101
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102
Prove that :In triangular series1 = 11+2 = 31+2+3 = 61+2+3+4 = 10…………..Triangular number in 8n+1 always form perfect square .
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105
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107