Задача 3.

Which of the following binary relations are reflexive? symmetric? transitive? equivalence relations? (The condition of $a \sim b$ is given in quotation marks.) 1) $a \sim b$ for any $a,b \in M$, on $M$; 2) $\varnothing$ on $M$; 3) "$a\mid b$" on the set of natural numbers; 4) "$a$ and $b$ can be connected by a path" on the set of vertices of a graph; 5) "$A \subset B$" on the set of all subset of a given set; 6) "$a$ and $b$ have the same remainder when dividing by $2$" on the set of natural numbers; 7) "$a$ and $b$ have the same last digit" on the set of natural numbers; 8) "$a$ and $b$ are in the same class" on the set of all students in high school; 9) "$a$ and $b$ were born in the same month" on the set of all people on Earth; 10) "there is a bijection between $a$ and $b$" on the set of all subsets of the natural numbers; 11) "$a>b$" on the set of natural numbers; 12) choose $X \subset M$. "$a \sim b$ if and only if $a,b \in X$", on $M$; 13) "$a$ and $b$ are citizens of the same country" on the set of all people on Earth; 14) "three sides of a triangle are equal to three sides of the other triangle" on the set of all tringles on a plane; 15) relation on the set of natural numbers made up by you; 16) relation on the set of all people on Earth made up by you.