Prove thate: A , B and C . - Vidyadip

Question

Prove thate: $\text{A}\subseteq\text{B},\ \text{B}\subseteq\text{C}$ and $\text{C}\subseteq\text{A}\Rightarrow\text{A}\subseteq\text{C}.$

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Answer

We have $\text{A}\subseteq\text{B},\ \text{B}\subseteq\text{C}$ and $\text{C}\subseteq\text{A},$ so $\text{A}\subseteq\text{B}\subseteq \text{C}\subseteq\text{A}$
Now, A is a subset of B and B is a subset of C, so A is a subset of C, i.e., $\text{A}\subseteq\text{C}$
Also, $\text{C}\subseteq\text{A}$
Hence, $\text{A}\subseteq\text{C}.$

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