Which of the following statements are true? Justify your answers. (This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. For instance, to show that "{1, padma, blue) is a set' is true, you need to say that this is true because it is a well-defined collection of 3 objects.)
i) The collection of Venn diagrams is a set.
ii) for any three sets B,A and C .
iii)
iv) , has a root in R only if m is an odd number.
v)
vi) Any system of three linear equations in two variables has no solution
vii) If a matrix has 2 n entries, where n ∈ N , then it is a square matrix.
viii) For n > 4 , the AM of the first n natural numbers is greater than n +1
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egers Write an odd natural number as a sum of two int m and 1 m in a way that 2 m is maximum.
The annual bonus given to the employees of a company is 10% of their taxable incomes, after the state and central taxes are deducted. The state tax is 15% of taxable income. The central tax is 15% of taxable income after deducting the state tax. Formulate this situation for determining the bonus, as a linear system.
Express z = 2/-4-i in standard (algebraic) form. Further, give an Argand diagram in which z, Z and -z are plotted.
Apply the Gaussian elimination process to determine values of λ for which the following linear system is consistent:
x-3y+4=0, 3x - 2y = λ, y = 6-2x.
जो निकाय आपने 5 (क) में प्राप्त किया है उसे प्रतिस्थापन द्वारा हल कीजिए।
Prove that
मान लीजिए कि इस प्रकार है कि
तथा
है। तब, दर्शाइए कि