Previous GATE Questions in Discrete Mathematics

26 votes
8 answers
151
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to$A \cup B$$A^c \cup ...
19 votes
3 answers
152
11 votes
3 answers
153
27 votes
5 answers
154
Let $G_1$ and $G_2$ be subgroups of a group $G$.Show that $G_1 \cap G_2$ is also a subgroup of $G$.Is $G_1 \cup G_2$ always a subgroup of $G$?.
21 votes
3 answers
155
Obtain the principal (canonical) conjunctive normal form of the propositional formula $$(p \wedge q) \vee (\neg q \wedge r)$$ where $\wedge$ is logical and, $\vee$ is inc...
33 votes
5 answers
159
The minimum number of edges in a connected cyclic graph on $n$ vertices is:$n-1$$n$$n+1$None of the above
24 votes
6 answers
160
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is:$2$$4$$8$None of the above
28 votes
6 answers
161
3 votes
0 answers
162
18 votes
2 answers
163
Use the patterns given to prove that$\sum\limits_{i=0}^{n-1} (2i+1) = n^2$(You are not permitted to employ induction)Use the result obtained in (A) to prove that $\sum\li...
22 votes
3 answers
164
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$is True or False.
21 votes
5 answers
165
17 votes
4 answers
166
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
19 votes
3 answers
167
31 votes
4 answers
168
23 votes
3 answers
169
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
39 votes
4 answers
170