Logic and sets


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Problem description Progress
ID 39025. Sections - 02
Темы: USE    Logic and sets   

Two segments are given on the number line: B = [10; 35] and C = [25; 49]. Specify the largest possible length of such segment A for which the logical expression

\((x \in A) \rightarrow \neg((x \in B) \equiv (x \in C) )\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39024. Sections - 01
Темы: USE    Logic and sets   

Two segments are given on the number line: B = [10; 20] and C = [12; 30]. Specify the smallest possible length of such a segment A for which the logical expression

\((x \notin B) \rightarrow ((x \in C) \rightarrow (x \in B)) \ vee \neg((x \notin A) \wedge (x \in C))\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39030. Sections - 03
Темы: USE    Logic and sets   

Two segments are given on the number line: B = [10; 40] and C = [15; 50]. Specify the smallest possible length of such a segment A for which the logical expression

\(((x \notin A) \wedge (x \in B)) \rightarrow ((x \in C) \rightarrow (x \in A))\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39031. Sections - 04
Темы: USE    Logic and sets   

Three segments are given on the number line: B = [5; 30], C = [1; 20] and D = [25; 45]. Specify the largest possible length of such segment A for which the logical expression

\((x \in A) \rightarrow (((x \notin B) \vee (x \notin C)) \rightarrow (x \in D))\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39078. Sections - 05
Темы: USE    Logic and sets   

Two segments are given on the number line: B = [5; 15], C = [30; 60]. Specify the smallest possible length of such a segment A for which the logical expression

\((x \notin A) \rightarrow \neg((x \in B) \wedge (x \notin C) \vee (x \in C))\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39079. Sections - 06
Темы: USE    Logic and sets   

Two segments are given on the number line: B = [40; 80], C = [120; 150]. Specify the largest possible length of such segment A for which the logical expression

\((((x \notin C)\rightarrow (x \in B)) \rightarrow (x \in B) ) \rightarrow ((x \notin A) \vee (x \in B))\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39080. Sections - 07
Темы: USE    Logic and sets   

Three segments are given on the number line: B = [0; 50], C = [25; 60] and D = [35; 80]. Specify the largest possible length of such segment A for which the logical expression

\((x \in A) \rightarrow ((x \in B) \vee (x \in D)) \ wedge (x \notin C)\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39081. Sections - 08
Темы: USE    Logic and sets   

Three segments are given on the number line: B = [0; 70], C = [30; 60] and D = [20; 90]. Specify the smallest possible length of such a segment A for which the logical expression

\((((x \in B) \rightarrow (x \in C)) \wedge (x \in D) ) \rightarrow (x \in A)\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39082. Sections - 09
Темы: USE    Logic and sets   

Three segments are given on the number line: B = [10; 40], C = [20; 85] and D = [70; 90]. Specify the largest possible length of such segment A for which the logical expression

\((x \in A) \rightarrow ((x \notin B) \rightarrow ((x \in C) \ wedge (x \in D)))\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39083. Segments - 10
Темы: USE    Logic and sets   

There are three segments on the number line: B = [25; 80], C = [60; 75] and D = [35; 70]. Specify the smallest possible length of such a segment A for which the logical expression

\(((x \in C) \neq (x \in B)) \rightarrow (x \in D) \ vee (x \in A)\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39084. Sections - 11
Темы: USE    Logic and sets   

There are three segments on the number line: B = [25; 80], C = [60; 75] and D = [70; 90]. Specify the smallest possible length of such a segment A for which the logical expression

\(((x \in C) \neq (x \in B)) \rightarrow (x \in D) \ vee (x \in A)\)
true (i.e. takes the value 1) for any value of the variable x.
ID 39721. Dividers with range - 01
Темы: USE    Logic and sets   

Let us denote by DIV(n, m) the statement "a natural number n is divisible without remainder by a natural number m". For what is the smallest natural number A< /code> boolean expression

\((DIV(x, 7) \rightarrow \neg DIV(x, 10)) \vee (x+A\ geq 100)\)
identically true (i.e. takes the value 1) for any integer natural value of the variable х.
ID 39722. Dividers with range - 03
Темы: USE    Logic and sets   

Let us denote by DIV(n, m) the statement "a natural number n is divisible without remainder by a natural number m". For what is the smallest natural number A< /code> boolean expression

\((x \geq 8) \rightarrow ( \neg DIV(x, 3) \rightarrow DIV(x, 2)) \vee (x+A\geq 25)\)
identically true (i.e. takes the value 1) for any integer natural value of the variable х.
ID 39723. Dividers with range - 02
Темы: USE    Logic and sets   

Let us denote by DIV(n, m) the statement "a natural number n is divisible without remainder by a natural number m". For what is the largest natural number A< /code> boolean expression

\((DIV(x, 7) \rightarrow \neg DIV(x, 10)) \vee (x-A\geq 10 )\)
identically true (i.e. takes the value 1) for any integer natural value of the variable х.
ID 39724. Dividers with range - 04
Темы: USE    Logic and sets   

Let us denote by DIV(n, m) the statement "a natural number n is divisible without remainder by a natural number m". For what is the largest natural number A< /code> boolean expression

\((x \geq 15) \rightarrow ( \neg DIV(x, 3) \rightarrow DIV(x, 2)) \vee (x-A\geq 10)\)
identically true (i.e. takes the value 1) for any integer natural value of the variable х.
ID 39725. Dividers with range - 05
Темы: USE    Logic and sets   

Let us denote by DIV(n, m) the statement "a natural number n is divisible without remainder by a natural number m". For what is the smallest natural number A< /code> boolean expression

\((x < 100) \rightarrow ((\neg DIV(x, 3) \wedge \neg DIV(x , 4))\rightarrow DIV(x, 5)) \vee (x+A\geq 60)\)
identically true (i.e. takes the value 1) for any integer natural value of the variable х.
ID 39726. Dividers with range - 06
Темы: USE    Logic and sets   

Let us denote by DIV(n, m) the statement "a natural number n is divisible without remainder by a natural number m". For what is the largest natural number A< /code> boolean expression

\((x < 100) \rightarrow (( DIV(x, 3) \wedge DIV(x, 4)) \rightarrow \neg DIV(x, 5)) \vee (x-A\geq 25)\)
identically true (i.e. takes the value 1) for any integer natural value of the variable х.