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First Year Math Sets, Functions & Groups


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Class 9Class 10First YearSecond Year
Mathcaret
Number Systems

672 Doubt Solutions

Sets, Functions & Groups

1344 Doubt Solutions

Matrices and Determinants

2016 Doubt Solutions

Quadratic Equations

2688 Doubt Solutions

Partial Fractions

3360 Doubt Solutions

Sequences and Series

4032 Doubt Solutions

Permutation, Combination and Probability

4704 Doubt Solutions

Mathematical Induction and Binomial Theorem

5376 Doubt Solutions

Fundamentals of Trigonometry

6048 Doubt Solutions

Trigonometric Identities

6720 Doubt Solutions

Trigonometric Functions And Their Graphs

7392 Doubt Solutions

Application of Trigonometry

8064 Doubt Solutions

Inverse Trigonometric Functions

8736 Doubt Solutions

Solutions Of Trigonometric Equations

9408 Doubt Solutions

Physicscaret
Chemistrycaret
5. Which of the following binary operations shown in tables (a) and (b) is commutative?\begin{tabular}{|c|c|c|c|c|}\hline 萬 & a & b & c & d \\\hline a & a & c & b & d \\\hline b & b & c & b & a \\\hline c & c & d & b & c \\\hline d & a & a & b & b \\\hline\end{tabular}\begin{tabular}{|c|c|c|c|c|}\hline 䒝 & a & b & c & d \\\hline a & a & c & b & d \\\hline b & c & d & b & a \\\hline c & b & b & a & c \\\hline d & d & a & c & d \\\hline\end{tabular}(a)(b)
7. Show that the set consisting of elements of the form a+\sqrt{3} b ( a b being rational) is an abelian group w.r.t. addition.
7. Show that the set consisting of elements of the form a+\sqrt{3} b ( a b being rational) is an abelian group w.r.t. addition.

7.Showthatthesetconsistingofelementsoftheforma+3b(abbeingrational)isanabeliangroupw.r.t.addition.7. Show that the set consisting of elements of the form a+\sqrt{3} b ( a b being rational) is an abelian group w.r.t. addition.

Example 1: Ordinary addition multiplication are operations on N . i.e. N is closed with respect to ordinary addition and multiplication because\[\forall a b \in N a+b \in N \wedge a . b \in N\]( \forall stands for" for all" and \wedge stands for" and")
Example 1: Ordinary addition multiplication are operations on N . i.e. N is closed with respect to ordinary addition and multiplication because\[\forall a b \in N a+b \in N \wedge a . b \in N\]( \forall stands for" for all" and \wedge stands for" and")

Example 1: Ordinary addition multiplication are operations on N . i.e. N is closed with respect to ordinary addition and multiplication because\[\forall a b \in N a+b \in N \wedge a . b \in N\]( \forall stands for" for all" and \wedge stands for" and")

4. Write two proper subsets of each of the following sets: -vii) W
4. Write two proper subsets of each of the following sets: -vii) W

4.Writetwopropersubsetsofeachofthefollowingsets:−vii)W4. Write two proper subsets of each of the following sets: -vii) W

4. Determine whether each of the following is a tautology a contingency or an absurdity: -ii) p \rightarrow(q \rightarrow p)
4. Determine whether each of the following is a tautology a contingency or an absurdity: -ii) p \rightarrow(q \rightarrow p)

4.Determinewhethereachofthefollowingisatautologyacontingencyoranabsurdity:−ii)p→(q→p)4. Determine whether each of the following is a tautology a contingency or an absurdity: -ii) p \rightarrow(q \rightarrow p)

Example 4: If B=\{123\} then\[P(B)=\{\Phi\{1\}\{2\}\{3\}\{12\}\{13\}\{23\}\{123\}\}\]
Example 4: If B=\{123\} then\[P(B)=\{\Phi\{1\}\{2\}\{3\}\{12\}\{13\}\{23\}\{123\}\}\]

Example 4: If B=\{123\} then\[P(B)=\{\Phi\{1\}\{2\}\{3\}\{12\}\{13\}\{23\}\{123\}\}\]

4. Write two proper subsets of each of the following sets: -ii) \{01\}
4. Write two proper subsets of each of the following sets: -ii) \{01\}

4.Writetwopropersubsetsofeachofthefollowingsets:−ii){01}4. Write two proper subsets of each of the following sets: -ii) \{01\}

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