Set Theory & Algebra

June 21, 2015 by Arjun Suresh 3 Comments

Syllabus

Sets, relations, functions, partial orders and lattices. Monoids, Groups.

“Monoids is an addition but it was already implied in Groups.”

Book

Video

Web Links

Previous Year Questions

http://gateoverflow.in/tag/set-theory%26algebra

Important Questions

http://gateoverflow.in/blog/16/important-questions-in-set-theory-%26-algebra

Recommended Tests

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Everything you need to know about LINE GRAPHS You won’t find anything better than this anywhere as its from NPTEL IIT MADRAS. [...]

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For access control Ethernet(802.3) uses CSMA/CD. In CSMS/CD collision is resolved by binary backoff algorithm which says if a collision occurs then the stations which involved in collision have to wait $wait = k * Time$ here K is a number chosen from ($0 - 2^n-1$) n is collision number as A has Successfully Transmit 1 packet and B has undergone first collision when A and B collide again for B second collision happened as for A new packets ! collision occurred A can wait between (0 or 1) before retransmission B can wait between (0-3) before retransmission (as it… [...]

Answered: NIELIT 2019 Feb Scientist D - Section D: 30

$\textrm{Given that:}$ $log_{10}(2^x+x-41)=x(1-log_{10}5)$ $\because log_aa=1$ $\textrm{We can use this property here, $log_{10}10=1$}$ $\implies$ $log_{10}(2^x+x-41)=x(log_{10}10-log_{10}5)$ $\implies$ $log_{10}(2^x+x-41)=x(log_{10}(\frac{10}{5}))$ $(\because log_ax-log_ay=log_a(\frac{x}{y}))$ $\implies$ $log_{10}(2^x+x-41)=x(log_{10}2)$ $\implies$ $log_{10}(2^x+x-41)=log_{10}2^x$ $(\because log_ax^n=n*log_ax)$ $\textrm{compair both side we get:}$ $\implies$ $2^x+x-41=2^x$ $\implies$ $x=41$ $\textrm{Option b is correct.}$ [...]

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$\textrm{Given that:}$ $x=\frac{\sqrt10+\sqrt2}{2},y=\frac{\sqrt10-\sqrt2}{2}$ $\textrm{first find $x^2+xy+y^2$}$ $\implies$ $x^2+xy+y^2+xy-xy$ $\implies$ $x^2+2xy+y^2-xy$ $\implies$ $(x+y)^2-xy….(1)$ $\textrm{Let find x+y first:}$ $\implies$ $\frac{\sqrt10+\sqrt2}{2}+\frac{\sqrt10-\sqrt2}{2}$ $\implies$ $\frac{2*\sqrt10}{2}$ $\implies$ $x+y=$ $\sqrt10...(2)$ $\textrm{Let find x*y:}$ $\implies$ $\frac{\sqrt10+\sqrt2}{2}*\frac{\sqrt10-\sqrt2}{2}$ $\implies$ $\frac{(10-2)}{4}$ $\implies$ $x*y=$$2...(3)$ $\textrm{Substitute eq (2) &(3) into (1), we get:}$ $\implies$ $(\sqrt{10})^2-2$ $\implies$ $8$ $\textrm{Now find l$og_2(8)$,which is equal to 3}$ $\textrm{Option D is correct.}$ [...]

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$\textrm{Given that: }$ $a^x=b ….(1)$ $b^y=c ….(2)$ $c^z=a….(3)$ $\textrm{taking log in above equations we get:}$ $\implies$ $xlog_2a=log_2b$ $\implies$ $x=\frac{log_2b}{log_2a}….(4)$ $\textrm{in the same way}$ $y=\frac{log_2c}{log_2b}….(5)$ $z=\frac{log_2a}{log_2c}…..(6)$ $\textrm{multiply equations (4),(5),(6).}$ $\implies$ $x*y*z=\frac{log_2b}{log_2a}*\frac{log_2c}{log_2b}*\frac{log_2a}{log_2c}$ $\implies$ $x*y*z=1$ $\textrm{Option C is correct.}$ [...]

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Answered: NIELIT 2019 Feb Scientist D - Section C: 21

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